De Moivre's theorem in Cartesian form.

[goodluck90]

Hey Guys,

I've been passed this from a friend to help them out, but I don't know much about it. So this is a bit of annoying first post... SORRY!

Homework Statement

if z = √2 + i, use de Moivre's theorem to find z^5 in Cartesian form.


AND.

Convert z = -8 + 8 √3 i to polar form.

Homework Equations

The Attempt at a Solution

No attempt - I know that's really cheeky, but it's not my work :(

 

[lineintegral1]

Um, have you asked your friend if they've attempted to apply the formulae they've been given? De Moivre's formula is (\cos x+i\sin x)^n=\cos (nx)+i\sin(nx). The value for z that your friend has been given should be converted to work with the formula. Also, the second value for z can easily be converted to polar coordinates given a geometric understanding of complex numbers. I won't give the answers; it is difficult to tell how much to help if I have know information as to how your friend has progressed.

Just as an edit, let me just say that, given Euler's formula, converting back and forth between polar and cartesian form should be relatively trivial. If this doesn't make sense, let me know.

 

[goodluck90]

Um, have you asked your friend if they've attempted to apply the formulae they've been given? De Moivre's formula is (\cos x+i\sin x)^n=\cos (nx)+i\sin(nx). The value for z that your friend has been given should be converted to work with the formula. Also, the second value for z can easily be converted to polar coordinates given a geometric understanding of complex numbers. I won't give the answers; it is difficult to tell how much to help if I have know information as to how your friend has progressed.

Just as an edit, let me just say that, given Euler's formula, converting back and forth between polar and cartesian form should be relatively trivial. If this doesn't make sense, let me know.

Yeah - I can understand how it doesn't help much - that's all the information I was given 'I can't do these two questions'.