Question

(2+3i)^6

Using Demoirves Theorem.

I tried solving it out, but somehow it didn't work for me.

(2+3i)^6
r=|z|=square root of 2^2 + 3^2 = square root of 13

z = square root of 13 *
(cos____ + isin_______ )

At this point I am stuck, so can someone help me?

Answer 1

let z = 2 + 3i
for the angle, tanØ = 3/2
Ø = .98279 radians

so z = √13(cos .98279 + isin .98279)

then z^6
= √3^6(cos 6(.98279) + isin 6(.98279) )
= 27(cos 5.89676 + i sin 5.89676)

= appr 25 - 10.18 i

or in short form:
27 cis 5.89676

If you need the answer is terms of degrees, set your calculator to degrees and repeat my steps

Answer 2

Thank you so much Reiny! I finally understand it!

Answer 3

somehow the √13 became √3, but I'm sure David can fix that, eh?