The equation whose solutions are the non-zero solutions of the eq… - Vidyadip

MCQ

The equation whose solutions are the non-zero solutions of the equation $\bar{z}=i z^2$, is

✓
$z^3+ i =0$
B
$z^3+z+1=0$
C
$z^3-i=0$
D
$z^3+i z+1=0$

✓

Answer

Correct option: A.

$z^3+ i =0$

(A)
$\overline{ z }= iz ^2$
Taking modulus on both sides, we get
$|\bar{z}|=\left|z^2\right|$
$\Rightarrow|z|=|z|^2$
$\Rightarrow| z |(| z |-1)=0$
$\Rightarrow|z|=1 \quad \ldots[\because|z| \neq 0]$
$\overline{ z }= iz ^2$
$\Rightarrow z \overline{ z }= iz ^3$
$\Rightarrow| z |^2= iz ^3$
$\Rightarrow iz ^3=1$
$\Rightarrow z ^3=- i$
$\Rightarrow z ^3+ i =0$

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