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Question: If \(z = x + iy\) and \(iz^{2} - \bar{z} = 0\), then \| z \| is equal to...

If z=x+iyz = x + iy and iz2−zˉ=0iz^{2} - \bar{z} = 0, then | z | is equal to

A

1

B

0 or 1

C

1 or 2

D

2

Answer

0 or 1

Explanation

Solution

Sol. iz2=zˉ⇒∣iz2∣=∣zˉ∣⇒∣z∣2=∣z∣⇒∣z∣(∣z∣−1)=0⇒∣z∣=0iz^{2} = \bar{z} \Rightarrow |iz^{2}| = |\bar{z}| \Rightarrow |z|^{2} = |z| \Rightarrow |z|(|z| - 1) = 0 \Rightarrow |z| = 0

or | z | = 1