# Complex numbers. write equation on form "a+bi"

Tags:
1. Sep 1, 2016

### terhje

1. The problem statement, all variables and given/known data
Write this complex number in the form "a+bi"
a) cos(-pi/3) + i*sin(-pi/3)
b) 2√2(cos(-5pi/6)+i*sin(-5pi/6))
2. Relevant equations
my only problem is that im getting + instead of - on the cosinus side.(real number)

3. The attempt at a solution
a) pi/3 in the unit circle is 1/2 for cosinus and √3)/2 for sinus, and since both have minus infront it should be
-1/2+-√3/2*i
the solution: 1/2-√3/2*i

b) exactly the same on b. -5pi/6 in the unit circle is -√3/2 for cos, and 1/2 for sin.
2√2*-(-√3/2) + i*2√2*-1/2
removing two's over and under. √2*√3-√2*i
my answer : = √6 -√2*i
the solution is -√6 -√2*i

sorry to bother,
thanks, T

2. Sep 1, 2016

### Aniruddha@94

What is $cos(-\theta)$?
Edit: And $sin(-\theta)$

Last edited: Sep 1, 2016
3. Sep 1, 2016

### terhje

lol, thanks for the help :D