Answer:
(a) r = 57.628
θ = 51.34°
(b) r = 0.711
θ = 38.65°
Step-by-step explanation:
(a) Let's assume
z = (5 + 4)(4 +5j)
= 9 x (4+5j)
= 36 + 45j
magnitude of z can be given by
[tex]\left | z \right |\ =\ r\ =\sqrt{36^2+45^2}[/tex]
=> r =57.628
angle of z can be given by,
[tex]tan\theta\ =\ \dfrac{45}{36}[/tex]
[tex]=>\ tan\theta=\ \dfrac{5}{4}[/tex]
[tex]=>\ \theta\ =\ tan^{-1}\dfrac{5}{4}[/tex]
θ = 51.34°
(b) Let's assume
[tex]z =\ \dfrac{(5 +4j)}{5+4}[/tex]
[tex]=\ \dfrac{(5+4j)}{9}[/tex]
[tex]=\ \dfrac{5}{9}+\dfrac{4i}{9}[/tex]
magnitude of z can be given by
[tex]\left | z \right |=\ r=\sqrt{(\dfrac{5}{9})^2+(\dfrac{4}{9})^2}[/tex]
[tex]=> r =\dfrac{\sqrt{41}}{9}[/tex]
=> r = 0.711
angle of z can be given by,
[tex]\ tan\theta\ =\ \dfrac{\dfrac{4}{9}}{\dfrac{5}{9}}[/tex]
[tex]=>\ tan\theta=\ \dfrac{4}{5}[/tex]
[tex]=>\ \theta\ =\ tan^{-1}\dfrac{4}{5}[/tex]
=> θ = 38.65°
