Question

If z and w are two complex numbers, prove that
lz + wl^2 = Izl^2 + lwl^2 + 2 Re(z w)
a.​

Answer 1

Step-by-step explanation:

Let ∣z∣=r ∴z=re

iθ

∣w∣=

r

1

∴w=

r

1

e

iϕ

arg z−arg w=

2

π

θ−ϕ=

2

π

θ=

2

π

+ϕ

z

w

ˉ

=re

iθ

⋅

r

1

e

−iϕ

=e

i(

2

π

+ϕ)

⋅e

−iϕ

=i.