Q. 44.3( 7 Votes )

# If z1 and z2 are two complex number such that |z1| = |z2| and arg (z1) + arg (z2) = π, then show that

Given:

|z1|=|z2| and arg(z1)+arg(z2)=

Let us assume arg(z1)=θ

arg(z2)=

We know that z=|z|(cosθ+isinθ)

z1=|z1|(cosθ+isinθ)-----------------(1)

z2=|z2|(cos(-θ)+isin(-θ))

z2=|z2|(-cosθ+isinθ)

z2=-|z2|(cosθ-isinθ)

Now we find the conjugate of z2

=-|z2|(cosθ+isinθ) ( )

Now,

( |z1|=|z2|)

z1=-

Thus proved.

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