Rationalizing complex numbers when the denominator has a (+ 1) added to it
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If I were to try and rationalize a complex number like $Z + 2W + 3 over Z + 1$, when I multiply by the conjugate of Z to make the denominator a real number, do I have to write z(conjugate)/z(conjugate) or z(conjugate) + 1/z(conjugate) + 1 or z(conjugate) - 1/z(conjugate) - 1??
(I'm sorry idk how to format the conjugate can someone help edit)
complex-numbers
edited Nov 21 at 10:50
José Carlos Santos
147k22117218
asked Nov 21 at 10:45
ming
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add a comment |
up vote
0
down vote
favorite
If I were to try and rationalize a complex number like $Z + 2W + 3 over Z + 1$, when I multiply by the conjugate of Z to make the denominator a real number, do I have to write z(conjugate)/z(conjugate) or z(conjugate) + 1/z(conjugate) + 1 or z(conjugate) - 1/z(conjugate) - 1??
(I'm sorry idk how to format the conjugate can someone help edit)
complex-numbers
edited Nov 21 at 10:50
José Carlos Santos
147k22117218
asked Nov 21 at 10:45
ming
1815
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
If I were to try and rationalize a complex number like $Z + 2W + 3 over Z + 1$, when I multiply by the conjugate of Z to make the denominator a real number, do I have to write z(conjugate)/z(conjugate) or z(conjugate) + 1/z(conjugate) + 1 or z(conjugate) - 1/z(conjugate) - 1??
(I'm sorry idk how to format the conjugate can someone help edit)
complex-numbers
edited Nov 21 at 10:50
José Carlos Santos
147k22117218
asked Nov 21 at 10:45
ming
1815
If I were to try and rationalize a complex number like $Z + 2W + 3 over Z + 1$, when I multiply by the conjugate of Z to make the denominator a real number, do I have to write z(conjugate)/z(conjugate) or z(conjugate) + 1/z(conjugate) + 1 or z(conjugate) - 1/z(conjugate) - 1??
(I'm sorry idk how to format the conjugate can someone help edit)
complex-numbers
complex-numbers
edited Nov 21 at 10:50
José Carlos Santos
147k22117218
asked Nov 21 at 10:45
ming
1815
edited Nov 21 at 10:50
José Carlos Santos
147k22117218
asked Nov 21 at 10:45
ming
1815
edited Nov 21 at 10:50
José Carlos Santos
147k22117218
edited Nov 21 at 10:50
José Carlos Santos
147k22117218
edited Nov 21 at 10:50
José Carlos Santos
147k22117218
147k22117218
asked Nov 21 at 10:45
ming
1815
asked Nov 21 at 10:45
ming
1815
asked Nov 21 at 10:45
ming
1815
1815
add a comment |
add a comment |
1 Answer
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If $Z,Winmathbb{C}$ (and $Zneq-1$) and if you wish to express $dfrac{Z+2W+3}{Z+1}$ has a quotient whose denominator is a real number, the natural option consists in multiplying both numerator and denominator with $overline{Z+1}$, thereby getting$$frac{Z+2W+3}{Z+1}=frac{(Z+2W+3)left(overline{Z+1}right)}{(Z+1)left(overline{Z+1}right)}=frac{(Z+2W+3)left(overline Z+1right)}{lvert Z+1rvert^2}.$$
answered Nov 21 at 10:50
José Carlos Santos
147k22117218
add a comment |
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If $Z,Winmathbb{C}$ (and $Zneq-1$) and if you wish to express $dfrac{Z+2W+3}{Z+1}$ has a quotient whose denominator is a real number, the natural option consists in multiplying both numerator and denominator with $overline{Z+1}$, thereby getting$$frac{Z+2W+3}{Z+1}=frac{(Z+2W+3)left(overline{Z+1}right)}{(Z+1)left(overline{Z+1}right)}=frac{(Z+2W+3)left(overline Z+1right)}{lvert Z+1rvert^2}.$$
answered Nov 21 at 10:50
José Carlos Santos
147k22117218
add a comment |
up vote
1
down vote
If $Z,Winmathbb{C}$ (and $Zneq-1$) and if you wish to express $dfrac{Z+2W+3}{Z+1}$ has a quotient whose denominator is a real number, the natural option consists in multiplying both numerator and denominator with $overline{Z+1}$, thereby getting$$frac{Z+2W+3}{Z+1}=frac{(Z+2W+3)left(overline{Z+1}right)}{(Z+1)left(overline{Z+1}right)}=frac{(Z+2W+3)left(overline Z+1right)}{lvert Z+1rvert^2}.$$
answered Nov 21 at 10:50
José Carlos Santos
147k22117218
add a comment |
up vote
1
down vote
up vote
1
down vote
If $Z,Winmathbb{C}$ (and $Zneq-1$) and if you wish to express $dfrac{Z+2W+3}{Z+1}$ has a quotient whose denominator is a real number, the natural option consists in multiplying both numerator and denominator with $overline{Z+1}$, thereby getting$$frac{Z+2W+3}{Z+1}=frac{(Z+2W+3)left(overline{Z+1}right)}{(Z+1)left(overline{Z+1}right)}=frac{(Z+2W+3)left(overline Z+1right)}{lvert Z+1rvert^2}.$$
answered Nov 21 at 10:50
José Carlos Santos
147k22117218
If $Z,Winmathbb{C}$ (and $Zneq-1$) and if you wish to express $dfrac{Z+2W+3}{Z+1}$ has a quotient whose denominator is a real number, the natural option consists in multiplying both numerator and denominator with $overline{Z+1}$, thereby getting$$frac{Z+2W+3}{Z+1}=frac{(Z+2W+3)left(overline{Z+1}right)}{(Z+1)left(overline{Z+1}right)}=frac{(Z+2W+3)left(overline Z+1right)}{lvert Z+1rvert^2}.$$
answered Nov 21 at 10:50
José Carlos Santos
147k22117218
answered Nov 21 at 10:50
José Carlos Santos
147k22117218
answered Nov 21 at 10:50
José Carlos Santos
147k22117218
answered Nov 21 at 10:50
José Carlos Santos
147k22117218
147k22117218
add a comment |
add a comment |
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