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Q.

Let z=x+iy be a non-zero complex number such that z2=i|z|2, where i=-1, then z lies on the:

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a

line, y=-x

b

imaginary axis

c

real axis

d

line, y = x

answer is D.

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Detailed Solution

z2=i|z|2⇒x2-y2+i.2xy=ix2+y2⇒x2-y2=0,2xy=x2+y2⇒x2=y2,2xy=x2+y2 ⇒2xy=2x2⇒x=0 or x=y ⇒x=y(∵z≠0)

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