Записать комплексное число в тригонометрической форме

Question

Помогите решить

iq_185 · Accepted Answer

1) z = i 
   |z| = 1 
   θ = π/2 
   z = 1 (cos π⁄2 + i sin π⁄2) 
2) z = 4 + 4√3 i 
   |z| = 8 
   θ = π/3 
   z = 8 (cos π⁄3 + i sin π⁄3) 
3) z = 1 + i 
   |z| = √2 
   θ = π/4 
   z = √2 (cos π⁄4 + i sin π⁄4) 
4) z = 3√2 + 3√2 i 
   |z| = 6 
   θ = π/4 
   z = 6 (cos π⁄4 + i sin π⁄4) 
5) z = (5√3)/2 + (5/2) i 
   |z| = 5 
   θ = π/6 
   z = 5 (cos π⁄6 + i sin π⁄6)

panic_doctor · Answer

1) z = i = cos(pi/2) + i*sin(pi/2)
2) z =  4 + 4*sqrt(3)*i = 8*(1/2+i*sqrt(3)/2) = 8(cos(pi/3)+ i * sin(pi/3))
3) z = 1+i = sqrt(2) * (1/sqrt(2) + i*1/sqrt(2)) = sqrt(2) * (cos(pi/4) + i*sin(pi/4))
4) такой же пример как и 3) только на 3sqrt(2) домножить
5) z = 5sqrt(3)/2 + 5/2 i = 5*(sqrt(3)/2 + i*1/2) = 5*(cos(pi/6) + i*sin(pi/6))