find-Z-if-arg-z-3-pi-and-arg-z-i-pi-4-

Question Number 80889 by M±th+et£s last updated on 07/Feb/20

f i n d Z

i f a r g (z - 3) = π

a n d a r g (z + i) = \frac{π}{4}

Commented by mr W last updated on 07/Feb/20

z = 1

Commented by msup trace by abdo last updated on 08/Feb/20

\Rightarrow z - 3 = r e^{i π} = - r \Rightarrow z = 3 - r (r > 0)

a n d z + i = ρ e^{\frac{i π}{4}} = ρ (\frac{1}{\sqrt{2}} + \frac{i}{. \sqrt{2}}) \Rightarrow

z = \frac{ρ}{\sqrt{2}} + (\frac{ρ}{\sqrt{2}} - 1) i = 3 - r \Rightarrow

3 - r = \frac{ρ}{\sqrt{2}} a n d \frac{ρ}{\sqrt{2}} - 1 = 0 \Rightarrow

ρ = \sqrt{2} \Rightarrow 3 - r = 1 \Rightarrow r = 2 \Rightarrow z = 1

Commented by peter frank last updated on 08/Feb/20

t h a n k y o u