Question

Let z and, wbe two non-zero complex numbers such that |z| = |w| and arg(z) + arg(w) = π, then z equals

Answer 1

Answer:

Step-by-step explanation:

z=|z|(cosθ+isinθ) where θ=argz

If θ1=argw then θ=π−θ1

So , z=|w|{cos(π−θ1)+isin(π−θ1)

=|w|(−cosθ1+isinθ1)

=−|w|(cosθ1−isinθ1)

=−w¯¯¯¯

Answer : −w¯¯¯¯