# Complex numbers in polar form

## Homework Statement

Compute the 4th roots of -16 in both Cartesian and polar form and plot their positions in the complex plane.

## Homework Equations

z^1/n=(r^1/n)(e^i(theta)/n), (r^1/n)(e^i(theta)/n)(e^i2(pi)/n........

## The Attempt at a Solution

How do I find the value of r, and theta??

Cyosis
Homework Helper
Draw z=-16 in the complex plane. The distance from the origin to -16 in the complex plane is r and the angle between the positive real axis and the negative real axis rotating counter clock wise is $\theta$.

How do I draw -16 in the complex plane, when I don't know r or theta?

Cyosis
Homework Helper
Draw the the complex plane and put a dot where -16 is. Then calculate the distance and angle.

where is -16?

Cyosis
Homework Helper
Do you know where -16 is on the line of real numbers?

are you saying that the argument is zero and that the modulus is 16?

Cyosis
Homework Helper
The modulus is 16, but the argument is not 0. If the argument was 0 -16 would be placed on the positive real axis, which it clearly isn't.

okay so you think the argument in pi

that's not right

why are you wasting my time?

Cyosis
Homework Helper
Wasting your time? Why would that not be right? You may want to provide some arguments to why this is wrong.

Either way I can tell you that I am not wrong. Perhaps review the the relevant equation you posted before jumping the gun?

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Beacause the answer is apparently 2e^i((pi + 2kpi)/4) where K=0,1,2,3

that's why it wouldn't be right.

Beacause the answer is apparently 2e^i((pi + 2kpi)/4) where K=0,1,2,3

that's why it wouldn't be right.

So ...take one of these numbers (say the k=0 one), convert it to Cartesian form, and take its 4th power. You can then check for yourself whether it is right.

Cyosis
Homework Helper
Beacause the answer is apparently 2e^i((pi + 2kpi)/4) where K=0,1,2,3

that's why it wouldn't be right.

It is obvious that every multiple of 2pi added to the original argument will return you to that exact same spot, after all a circle is exactly 2pi radians.