Homework Help: 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.

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