Question

Let z, w be two non zero complex number such that | z | = | w| & arg (z) + arg(w) = p then z =

• A. $\bar{w}$
• B. – $\bar{w}$
• C. w
• D. – w

Answer 1

Answer: (B)

– $\bar{w}$

Answer 2

Sol. arg (zw) = p Ž $zw = z.\bar{w}$ Ž zw.w = $\bar{z}\bar{w}.w$

Ž $z.w^{2} = \bar{z}.|w|^{2}$ Ž $zw^{2} = \bar{z}|z|^{2}$

Ž $zw^{2} = \bar{z}z\bar{z}$

Ž w² = $(\bar{z})^{2}$

Ž $\bar{z}$ = w or – w

Ž $z$ = $\bar{w}$ or –$\bar{w}$

but only $z$ = –$\bar{w}$ satisfies arg $(zw)$ = p