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Question: If z<sub>1</sub>, z<sub>2</sub> are any two complex numbers, then \(|z^{2}| = |\bar{z}|^{2}\) \(z = ...

If z1, z2 are any two complex numbers, then ∣z2∣=∣zˉ∣2|z^{2}| = |\bar{z}|^{2} z=zˉz = \bar{z} is equal to.

A

zˉ2=zˉ2{\bar{z}}^{2} = {\bar{z}}^{2}

B

∣z∣|z|

C

∣z+2z∣=2\left| z + \frac{2}{z} \right| = 2

D

3−1\sqrt{3} - 1

Answer

3−1\sqrt{3} - 1

Explanation

Solution

Sol. Trick : Check by putting =∣z1−z2∣∣z1−z2‾∣=∣z1−z2∣∣z1−z2∣=1= \frac{|z_{1} - z_{2}|}{|\overline{z_{1} - z_{2}}|} = \frac{|z_{1} - z_{2}|}{|z_{1} - z_{2}|} = 1and z1=r1z_{1} = r_{1}.