Question

Помогите решить записать эти 3 примера в тригонометрической форме. ( желательно с объяснениями ) 1) Z = √3 + i 2) Z = 10 3) Z = - 3 + 3 i.

Answer 1

Z = |z|(cos(a) + i*sin(a)) - тригонометрическая форма

1) |z| = √(3 + 1) = 2

cos(a) = √3/2
sin(a) = 1/2

a = π/6

z = 2(cos(π/6) + i*sin(π/6))

2) |z| = 10

cos(a) = 10/10 = 1
sin(a) = 0/10 = 0

a = 0

z = 10(cos(0) + i*sin(0))

3) |z| = √(9 + 9) = 3√2

cos(a) = (-3)/(3√2) = -√2/2
sin(a) = 3/(3√2) = √2/2

a = 3π/4

z = 3√2(cos(3π/4) + i*sin(3π/4))