AP EAMCET · Maths · Complex Number
If \(z=x+i y\) and \(z^2=(i \bar{z})^2\), then
- A \(y= \pm \frac{x}{\sqrt{3}}\)
- B \(y= \pm x\)
- C \(y= \pm \frac{x}{2}\)
- D \(x=0, y= \pm 1\)
Answer & Solution
Correct Answer
(B) \(y= \pm x\)
Step-by-step Solution
Detailed explanation
\(z^2=(i \bar{z})^2\) \(z^2 = i^2 (\bar{z})^2\) \(z^2 = - (\bar{z})^2\) \(z^2 + (\bar{z})^2 = 0\) \((x+iy)^2 + (x-iy)^2 = 0\) \((x^2-y^2+2ixy) + (x^2-y^2-2ixy) = 0\) \(2x^2 - 2y^2 = 0\) \(x^2 - y^2 = 0\) \(y^2 = x^2\) \(y = \pm x\)
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