# Changing complex numbers in form a+bi

1. Jun 7, 2012

### ME_student

1. The problem statement, all variables and given/known data
Here is the problem: ($\sqrt{}6$(cos(3pie/16)+i sin(3pie/16)))^4

2. Relevant equations

After 360*=2pier Do you add 2pier to the next degree which would be 30*=pie/6?

3. The attempt at a solution

2. Jun 7, 2012

### daveb

In situations such as these, it is usually easiest to convert to the exponential form and solve from there, then convert back to a+bi form.

3. Jun 7, 2012

### vela

Staff Emeritus
What do you mean by this? By "2pier" do you mean $2\pi$ radians or $2\pi r$, the circumference of a circle? What is "the next degree"? After 360 degrees, the next degree is 361 degrees, no?

4. Jun 7, 2012

### Muphrid

The greek letter $\pi$ is just spelled as "pi". It is not the same as the dish.

5. Jun 7, 2012

### ME_student

Sorry, I couldn't find the 2 "pie" r.

No worry guys I figured it out. Wish I could post pictures... I would show you how I solved it.

EDIT: Sweet I can post pics now!

6. Jun 8, 2012

### ME_student

Here is the problem

7. Jun 8, 2012

### Muphrid

Per daveb, I too think it would be much easier to convert to polar form first and then convert back. The reason is that the exponential lends itself to being raised to a power much more easily than the rectangular form.

What you get is

$$(\sqrt{6} e^{3\pi i/16})^4 = 36 e^{3\pi i/4}$$

This is what you got, after all, but you can do it in one line as opposed to resorting to a bunch of trig identities to square the rectangular form.

8. Jun 8, 2012

### ME_student

Apologies for the quality of the pictures...

9. Jun 10, 2012

### AmritpalS

Look up de Moivre's Theorem. It'll narrow down the tedious computation with multplying it out.

10. Jun 10, 2012

### BloodyFrozen

$$(cos(x)+i~sin(x))^{n} = cos(nx)+i~sin(nx)$$

11. Feb 6, 2014

### ME_student

Whoa... I was a member while taking trig, crazy!

12. Feb 7, 2014

### 2milehi

So much easier when using Euler's formula. I can do it in my head rather quickly.

13. Feb 7, 2014

### ME_student

Good for you.

14. Feb 8, 2014

### 2milehi

Just sayin' - if you recognize this

then the problem become easy to do. There are plenty of ways to skin the cat with this problem.