Motion of Point P in Complex Plane: Finding z(t)

[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?

 

[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

 

[rude man]

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?

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.)

 

[Deveno]

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.)

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.

 

[rude man]

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.

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?