Write the complex number z Squareroot 3 i in exact polar f

Write the complex number z = Squareroot 3 + i, in exact polar form with 0 lessthanorequalto theta lessthanorequalto 2 pi. Evaluate (1 + i)^20 using De Moivre\'s Theorem. Write your final answer in rectangular form. Let z_1 = 4(cos(120 degree) + i sin(120 degree)) and z_2 = 2(cos(30 degree) + i sin(30 degree)). Find z_1 z_2 and z_1/z_2.

Solution

1. z=sqrt3 +i

R=sqrt(3+1)=2

theta=tan^-1(1/sqrt3)=pi/6

required polar form

2(cos (pi/6)+i sin(pi/6))