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AP EAMCET · Maths · Complex Number

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

  1. A \(z^3+i=0\)
  2. B \(z^3+z+1=0\)
  3. C \(z^3-i=0\)
  4. D \(z^3+i z+1=0\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(z^3+i=0\)

Step-by-step Solution

Detailed explanation

\begin{array}{lccl}\text { } & \bar{z}=i z^2 & & \\ \Rightarrow & z=-i \bar{z}^2 & & \Rightarrow z=-i\left[i z^2\right]^2 \\ \Rightarrow & z=-i i^2 z^4 & & \Rightarrow z=i z^4 \\ \Rightarrow & z^4=\frac{1}{i} z & & z^4=-i z \\ \Rightarrow & z^4+i z=0 & & z z\left(z^3+i\right)=0…