Question

escrevs z= 2+2i na forma trigonométrica URGENTEEEE

Answer 1

z = 2 + 2i

a = 2 | b = 2

$p = \sqrt{a^{2} +(b)^{2} } \\ p = \sqrt{(2)^{2} +(2)^{2}} \\ p = \sqrt{2 * 2^{2} } \\ p = 2\sqrt{2}$

a = b

$cos\theta = \frac{a}{p} = \frac{2}{2\sqrt{2}} = \frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2}$

$\theta = 45^{o} \\ \\ \\ \frac{180}{45} = \frac{\pi }{x} \to x = \frac{\pi }{4}$

$\boxed{\mathsf{z = p(cos\theta +i \cdot sin\theta )}}$

$z = 2\sqrt{2}(cos\frac{\pi }{4} +i \cdot sin\frac{\pi }{4} )$