(C) Given the equation $\bar{z} = i z^2$. Taking the conjugate on both sides,we get $z = \bar{i} \bar{z}^2 = -i \bar{z}^2$. Substitute $\bar{z} = i z^

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(C) Given the equation $\bar{z} = i z^2$. Taking the conjugate on both sides,we get $z = \bar{i} \bar{z}^2 = -i \bar{z}^2$. Substitute $\bar{z} = i z^2$ into the equation: $z = -i (i z^2)^2$ $z = -i (i^2 z^4)$ $z = -i (-1) z^4$ $z = i z^4$ $z^4 - i z = 0$ $z (z^3 - i) = 0$ Since we are looking for non-zero solutions,$z \neq 0$,so $z^3 - i = 0$.

Class 11 Mathematics 1 Complex Numbers and Quadratic Equations: Complex Numbers Mix Examples-Complex numbers

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

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

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1 Complex Numbers and Quadratic Equations: Complex Numbers

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

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