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Let z be a non-zero complex number Then ...

Let z be a non-zero complex number Then what is `z^(-1)` (multiplicative inverse of z) equal to ?

A

`(vecz)/(|z|^(2))`

B

`(z)/(|z|^(2))`

C

`(vecz)/(|z|`

D

`(|z|)/(z)`

Text Solution

Verified by Experts

The correct Answer is:
A
Let z be a non-zero complex number, such that `z=x+iywhere x, y in R`
Then `z^(-1)(1)/(x+iy)`
So, `z^(-1)(x-iy)/((x+iy)(x-iy))=(x-iy)/(x^(2)+y^(2))=(barz)/(|z|^(2))`
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Knowledge Check

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