# Homework Help: Complex Number

1. Dec 18, 2011

### fizzo68

The motion of a point P in the complex plane is defined by the
principal root of z^5= (1+ t)^i

a)find z(t)
b)Show that P is undergoing a circular motion. Find the velocity
and acceleration as a function of time

I'm pretty sure I know how to do b but I don't really understand the wording of the question. A is really confusing me. The 'Principal root' would that mean I have to take the root of both sides? and then just rearrange and isolate z?

2. Dec 18, 2011

### ehild

The function z(t) describes the motion of the point in the x,y plane. So you need to take the fifth root of both sides of the equation to get z(t). As you know, there are 5 fifth roots of a complex number, you have to take the principal one.

ehild

3. Dec 18, 2011

### rude man

Ask Dr. Euler for help.

(I have to confess, I never heard the term 'principal root' before. I believe, with deep conviction , that all roots are created equal.)

4. Dec 18, 2011

### Deveno

well, there is a qualitative difference between the 2 roots of z4 - 1 = 0, 1 and i, in the sense that 1 is a power of i, but not vice versa.

5. Dec 18, 2011

### rude man

EIDT EDIT: Oops, I still get a straight line, magnitude [ln(1+t)]^0.2 and angle 0.2 rad.

Someone else please join in?

Last edited: Dec 18, 2011