Finding magnitude of a complex number












7















$$z = dfrac{2+2i}{4-2i}$$



$$|z| = ? $$




My attempt:



$$dfrac{(2+2i)(4+2i)}{(4-2i)(4+2i)} = dfrac{4+12i}{20} = dfrac{4}{20}+dfrac{12}{20}i = dfrac{1}{5} + dfrac{3}{5}i$$



Now taking its magnitude and we have that



$$|z| = sqrt{biggr (dfrac 1 5 biggr ) ^2 +biggr (dfrac 3 5 biggr )^2} = sqrt {dfrac 2 5 }$$



Am I right?










share|cite|improve this question





























    7















    $$z = dfrac{2+2i}{4-2i}$$



    $$|z| = ? $$




    My attempt:



    $$dfrac{(2+2i)(4+2i)}{(4-2i)(4+2i)} = dfrac{4+12i}{20} = dfrac{4}{20}+dfrac{12}{20}i = dfrac{1}{5} + dfrac{3}{5}i$$



    Now taking its magnitude and we have that



    $$|z| = sqrt{biggr (dfrac 1 5 biggr ) ^2 +biggr (dfrac 3 5 biggr )^2} = sqrt {dfrac 2 5 }$$



    Am I right?










    share|cite|improve this question



























      7












      7








      7








      $$z = dfrac{2+2i}{4-2i}$$



      $$|z| = ? $$




      My attempt:



      $$dfrac{(2+2i)(4+2i)}{(4-2i)(4+2i)} = dfrac{4+12i}{20} = dfrac{4}{20}+dfrac{12}{20}i = dfrac{1}{5} + dfrac{3}{5}i$$



      Now taking its magnitude and we have that



      $$|z| = sqrt{biggr (dfrac 1 5 biggr ) ^2 +biggr (dfrac 3 5 biggr )^2} = sqrt {dfrac 2 5 }$$



      Am I right?










      share|cite|improve this question
















      $$z = dfrac{2+2i}{4-2i}$$



      $$|z| = ? $$




      My attempt:



      $$dfrac{(2+2i)(4+2i)}{(4-2i)(4+2i)} = dfrac{4+12i}{20} = dfrac{4}{20}+dfrac{12}{20}i = dfrac{1}{5} + dfrac{3}{5}i$$



      Now taking its magnitude and we have that



      $$|z| = sqrt{biggr (dfrac 1 5 biggr ) ^2 +biggr (dfrac 3 5 biggr )^2} = sqrt {dfrac 2 5 }$$



      Am I right?







      complex-numbers






      share|cite|improve this question















      share|cite|improve this question













      share|cite|improve this question




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      edited Dec 4 at 13:46









      greedoid

      37.2k114794




      37.2k114794










      asked Dec 3 at 17:47









      Hamilton

      1838




      1838






















          2 Answers
          2






          active

          oldest

          votes


















          7














          Yes, you are. You can do it also like this: $$Big|{2+2iover 4-2i}Big|=Big|{1+iover 2-i}Big|={|1+i|over |2-i|}= {sqrt{2}over sqrt{5}}$$






          share|cite|improve this answer





























            3














            It is better to use $$left|dfrac abright|=dfrac{|a|}{|b|}$$



            $|2+2i|=sqrt{2^2+2^2}=2sqrt2$






            share|cite|improve this answer





















            • I first made the denominator real and then did my calculations to avoid any errors .
              – Hamilton
              Dec 3 at 17:55












            • @Hamilton, At least for modulus, the formula I believe is more suitable
              – lab bhattacharjee
              Dec 3 at 17:56










            • However, is it a bad way?
              – Hamilton
              Dec 3 at 18:11










            • Rationalization may be costly in some cases
              – lab bhattacharjee
              Dec 3 at 18:17










            • @Hamilton I'd say it depends whether you're interested in the actual value of $z$ or not. This way gets you straight to the magnitude and saves you the slightly more error-prone algebra of making a real denominator to get $z$.
              – timtfj
              Dec 3 at 19:53











            Your Answer





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            2 Answers
            2






            active

            oldest

            votes








            2 Answers
            2






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes









            7














            Yes, you are. You can do it also like this: $$Big|{2+2iover 4-2i}Big|=Big|{1+iover 2-i}Big|={|1+i|over |2-i|}= {sqrt{2}over sqrt{5}}$$






            share|cite|improve this answer


























              7














              Yes, you are. You can do it also like this: $$Big|{2+2iover 4-2i}Big|=Big|{1+iover 2-i}Big|={|1+i|over |2-i|}= {sqrt{2}over sqrt{5}}$$






              share|cite|improve this answer
























                7












                7








                7






                Yes, you are. You can do it also like this: $$Big|{2+2iover 4-2i}Big|=Big|{1+iover 2-i}Big|={|1+i|over |2-i|}= {sqrt{2}over sqrt{5}}$$






                share|cite|improve this answer












                Yes, you are. You can do it also like this: $$Big|{2+2iover 4-2i}Big|=Big|{1+iover 2-i}Big|={|1+i|over |2-i|}= {sqrt{2}over sqrt{5}}$$







                share|cite|improve this answer












                share|cite|improve this answer



                share|cite|improve this answer










                answered Dec 3 at 17:49









                greedoid

                37.2k114794




                37.2k114794























                    3














                    It is better to use $$left|dfrac abright|=dfrac{|a|}{|b|}$$



                    $|2+2i|=sqrt{2^2+2^2}=2sqrt2$






                    share|cite|improve this answer





















                    • I first made the denominator real and then did my calculations to avoid any errors .
                      – Hamilton
                      Dec 3 at 17:55












                    • @Hamilton, At least for modulus, the formula I believe is more suitable
                      – lab bhattacharjee
                      Dec 3 at 17:56










                    • However, is it a bad way?
                      – Hamilton
                      Dec 3 at 18:11










                    • Rationalization may be costly in some cases
                      – lab bhattacharjee
                      Dec 3 at 18:17










                    • @Hamilton I'd say it depends whether you're interested in the actual value of $z$ or not. This way gets you straight to the magnitude and saves you the slightly more error-prone algebra of making a real denominator to get $z$.
                      – timtfj
                      Dec 3 at 19:53
















                    3














                    It is better to use $$left|dfrac abright|=dfrac{|a|}{|b|}$$



                    $|2+2i|=sqrt{2^2+2^2}=2sqrt2$






                    share|cite|improve this answer





















                    • I first made the denominator real and then did my calculations to avoid any errors .
                      – Hamilton
                      Dec 3 at 17:55












                    • @Hamilton, At least for modulus, the formula I believe is more suitable
                      – lab bhattacharjee
                      Dec 3 at 17:56










                    • However, is it a bad way?
                      – Hamilton
                      Dec 3 at 18:11










                    • Rationalization may be costly in some cases
                      – lab bhattacharjee
                      Dec 3 at 18:17










                    • @Hamilton I'd say it depends whether you're interested in the actual value of $z$ or not. This way gets you straight to the magnitude and saves you the slightly more error-prone algebra of making a real denominator to get $z$.
                      – timtfj
                      Dec 3 at 19:53














                    3












                    3








                    3






                    It is better to use $$left|dfrac abright|=dfrac{|a|}{|b|}$$



                    $|2+2i|=sqrt{2^2+2^2}=2sqrt2$






                    share|cite|improve this answer












                    It is better to use $$left|dfrac abright|=dfrac{|a|}{|b|}$$



                    $|2+2i|=sqrt{2^2+2^2}=2sqrt2$







                    share|cite|improve this answer












                    share|cite|improve this answer



                    share|cite|improve this answer










                    answered Dec 3 at 17:51









                    lab bhattacharjee

                    222k15155273




                    222k15155273












                    • I first made the denominator real and then did my calculations to avoid any errors .
                      – Hamilton
                      Dec 3 at 17:55












                    • @Hamilton, At least for modulus, the formula I believe is more suitable
                      – lab bhattacharjee
                      Dec 3 at 17:56










                    • However, is it a bad way?
                      – Hamilton
                      Dec 3 at 18:11










                    • Rationalization may be costly in some cases
                      – lab bhattacharjee
                      Dec 3 at 18:17










                    • @Hamilton I'd say it depends whether you're interested in the actual value of $z$ or not. This way gets you straight to the magnitude and saves you the slightly more error-prone algebra of making a real denominator to get $z$.
                      – timtfj
                      Dec 3 at 19:53


















                    • I first made the denominator real and then did my calculations to avoid any errors .
                      – Hamilton
                      Dec 3 at 17:55












                    • @Hamilton, At least for modulus, the formula I believe is more suitable
                      – lab bhattacharjee
                      Dec 3 at 17:56










                    • However, is it a bad way?
                      – Hamilton
                      Dec 3 at 18:11










                    • Rationalization may be costly in some cases
                      – lab bhattacharjee
                      Dec 3 at 18:17










                    • @Hamilton I'd say it depends whether you're interested in the actual value of $z$ or not. This way gets you straight to the magnitude and saves you the slightly more error-prone algebra of making a real denominator to get $z$.
                      – timtfj
                      Dec 3 at 19:53
















                    I first made the denominator real and then did my calculations to avoid any errors .
                    – Hamilton
                    Dec 3 at 17:55






                    I first made the denominator real and then did my calculations to avoid any errors .
                    – Hamilton
                    Dec 3 at 17:55














                    @Hamilton, At least for modulus, the formula I believe is more suitable
                    – lab bhattacharjee
                    Dec 3 at 17:56




                    @Hamilton, At least for modulus, the formula I believe is more suitable
                    – lab bhattacharjee
                    Dec 3 at 17:56












                    However, is it a bad way?
                    – Hamilton
                    Dec 3 at 18:11




                    However, is it a bad way?
                    – Hamilton
                    Dec 3 at 18:11












                    Rationalization may be costly in some cases
                    – lab bhattacharjee
                    Dec 3 at 18:17




                    Rationalization may be costly in some cases
                    – lab bhattacharjee
                    Dec 3 at 18:17












                    @Hamilton I'd say it depends whether you're interested in the actual value of $z$ or not. This way gets you straight to the magnitude and saves you the slightly more error-prone algebra of making a real denominator to get $z$.
                    – timtfj
                    Dec 3 at 19:53




                    @Hamilton I'd say it depends whether you're interested in the actual value of $z$ or not. This way gets you straight to the magnitude and saves you the slightly more error-prone algebra of making a real denominator to get $z$.
                    – timtfj
                    Dec 3 at 19:53


















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