Question

Calculați modulul numărului complex: ((24-7i)/(20+15i))^4.
Mulțumesc!

Answer 1

$\Bigg|\Big(\dfrac{24-7i}{20+15i}\Big)^4\Bigg| = \Bigg|\dfrac{24-7i}{20+15i}\Bigg|^4 = \\ \\ = \Bigg(\dfrac{|24-7i|}{|20+15i|}\Bigg)^4 = \Bigg(\dfrac{\sqrt{27^2+(-7)^2}}{\sqrt{20^2+(15)^2}}\Bigg)^4=\Bigg(\dfrac{\sqrt{625}}{\sqrt{625}}\Bigg)^4 = 1^4 = \boxed{1}$

Answer 2

Răspuns:

Explicație pas cu pas: