Complex numbers: Calculate the multiplicative inverse for $z=a+bi neq 0$
$begingroup$
Complex numbers: Calculate the multiplicative inverse for $z=a+bi neq 0$
$a$ is the real part and $i$ is the imaginary one.
I tried this but not sure:
Inverse of $z$ is $z^{-1}=frac{1}{z}$ so
$$frac{1}{z}= frac{bar{z}}{zbar{z}}=frac{bar{z}}{a^{2}+b^{2}}=frac{a}{a^{2}+b^{2}}-frac{b}{a^{2}+b^{2}}i$$
Or is it done completely different?
complex-numbers
edited Nov 28 '16 at 21:38
Matthew Conroy
10.3k32836
asked Nov 28 '16 at 21:17
kathelkkathelk
447510
$endgroup$
add a comment |
$begingroup$
Complex numbers: Calculate the multiplicative inverse for $z=a+bi neq 0$
$a$ is the real part and $i$ is the imaginary one.
I tried this but not sure:
Inverse of $z$ is $z^{-1}=frac{1}{z}$ so
$$frac{1}{z}= frac{bar{z}}{zbar{z}}=frac{bar{z}}{a^{2}+b^{2}}=frac{a}{a^{2}+b^{2}}-frac{b}{a^{2}+b^{2}}i$$
Or is it done completely different?
complex-numbers
edited Nov 28 '16 at 21:38
Matthew Conroy
10.3k32836
asked Nov 28 '16 at 21:17
kathelkkathelk
447510
$endgroup$
2
$begingroup$
Yes your solution is correct
$endgroup$
– ziggurism
Nov 28 '16 at 21:18
2
$begingroup$
@kathelk Your answer is fine.
$endgroup$
– Olivier Oloa
Nov 28 '16 at 21:19
add a comment |
$begingroup$
Complex numbers: Calculate the multiplicative inverse for $z=a+bi neq 0$
$a$ is the real part and $i$ is the imaginary one.
I tried this but not sure:
Inverse of $z$ is $z^{-1}=frac{1}{z}$ so
$$frac{1}{z}= frac{bar{z}}{zbar{z}}=frac{bar{z}}{a^{2}+b^{2}}=frac{a}{a^{2}+b^{2}}-frac{b}{a^{2}+b^{2}}i$$
Or is it done completely different?
complex-numbers
edited Nov 28 '16 at 21:38
Matthew Conroy
10.3k32836
asked Nov 28 '16 at 21:17
kathelkkathelk
447510
$endgroup$
Complex numbers: Calculate the multiplicative inverse for $z=a+bi neq 0$
$a$ is the real part and $i$ is the imaginary one.
I tried this but not sure:
Inverse of $z$ is $z^{-1}=frac{1}{z}$ so
$$frac{1}{z}= frac{bar{z}}{zbar{z}}=frac{bar{z}}{a^{2}+b^{2}}=frac{a}{a^{2}+b^{2}}-frac{b}{a^{2}+b^{2}}i$$
Or is it done completely different?
complex-numbers
complex-numbers
edited Nov 28 '16 at 21:38
Matthew Conroy
10.3k32836
asked Nov 28 '16 at 21:17
kathelkkathelk
447510
edited Nov 28 '16 at 21:38
Matthew Conroy
10.3k32836
asked Nov 28 '16 at 21:17
kathelkkathelk
447510
edited Nov 28 '16 at 21:38
Matthew Conroy
10.3k32836
edited Nov 28 '16 at 21:38
Matthew Conroy
10.3k32836
edited Nov 28 '16 at 21:38
Matthew Conroy
10.3k32836
10.3k32836
asked Nov 28 '16 at 21:17
kathelkkathelk
447510
asked Nov 28 '16 at 21:17
kathelkkathelk
447510
asked Nov 28 '16 at 21:17
kathelkkathelk
447510
447510
2
$begingroup$
Yes your solution is correct
$endgroup$
– ziggurism
Nov 28 '16 at 21:18
2
$begingroup$
@kathelk Your answer is fine.
$endgroup$
– Olivier Oloa
Nov 28 '16 at 21:19
add a comment |
2
$begingroup$
Yes your solution is correct
$endgroup$
– ziggurism
Nov 28 '16 at 21:18
2
$begingroup$
@kathelk Your answer is fine.
$endgroup$
– Olivier Oloa
Nov 28 '16 at 21:19
2
2
$begingroup$
Yes your solution is correct
$endgroup$
– ziggurism
Nov 28 '16 at 21:18
$begingroup$
Yes your solution is correct
$endgroup$
– ziggurism
Nov 28 '16 at 21:18
2
2
$begingroup$
@kathelk Your answer is fine.
$endgroup$
– Olivier Oloa
Nov 28 '16 at 21:19
$begingroup$
@kathelk Your answer is fine.
$endgroup$
– Olivier Oloa
Nov 28 '16 at 21:19
add a comment |
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$begingroup$
Yes your solution is correct
$endgroup$
– ziggurism
Nov 28 '16 at 21:18
2
$begingroup$
@kathelk Your answer is fine.
$endgroup$
– Olivier Oloa
Nov 28 '16 at 21:19