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Q.

Suppose two complex numbers z = a + ib;w = c + id satisfy the equation z+wz=wz+w then

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a

at least one of b & d is non-zero

b

both a & c are zeros

c

both b & d must be non zeros

d

both b & d are zeros

answer is D.

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Detailed Solution

(z+w)2=zw⇒z2+zw+w2=0
Let zw=t⇒zw=−1±3i2 arg⁡z−arg⁡w=±2π3
tan−1⁡ba−tan−1⁡dc=±2π3⇒bc−adac+bd=±3

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