Single Choice

If $$z_1$$, $$z_2$$ are two complex number such that $$|z_1|=|z_2|$$ and arg $$z_1+ $$arg $$ z_2=0$$ then $$z_1$$, $$z_2$$ and

AEqual
BNot equal
CConjugate to each other
Correct Answer
DNeed not be conjugate

Solution

$$|z_{1}| =| z_{2}|$$
Also, $$arg(z_{1})=-arg(z_{2})$$
Hence, $$z_{1}$$ & $$z_{2}$$ lie on opposite side of real axis with same modulus
Hence, $$\left | z_{1}\right |=\left | z_{2} \right |$$ &
$$arg(z_{1})=\theta =-arg(z_{2})=-(-\theta )$$
$$\therefore z_{1}$$ & $$z_{2}$$ are conjugates of each other

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