Complex Number--De Moivres Theorm

**heatly** · July 29th 2010, 01:15 AM

Can any body help with this one.

Evaluate the following using De Moivres Theorm's.
(2+i)^3

**Ackbeet** · July 29th 2010, 01:35 AM

What have you done so far?

**Prove It** · July 29th 2010, 02:05 AM

Originally Posted by heatly

Can any body help with this one.

Evaluate the following using De Moivres Theorm's.
(2+i)^3

Start by converting $2 + i$ to Polar form...

**heatly** · July 29th 2010, 02:34 AM

I did that and got,
|2+i| = sqrt 5
z=(sqrt(5))^3 (cos pi/2 + i sin pi/2)
......
Which gives...0+11.18i ???

The ans is z= 2 + 11i

**Ackbeet** · July 29th 2010, 02:59 AM

I don't think you computed the angle correctly. Try $\theta=\tan^{-1}(\text{Im}(z)/\text{Re}(z)).$

**heatly** · July 29th 2010, 03:10 AM

thankyou very much you are correct Ackbeet.

**Ackbeet** · July 29th 2010, 03:26 AM

You're welcome. Have a good one!

Thread: Complex Number--De Moivres Theorm