# Show the real part is zero

• oab729
In summary, when the real part of a complex number is zero, it is purely imaginary and can be expressed as a multiple of the imaginary unit, i. To show that the real part is zero, the complex conjugate can be used. It is important to show that the real part is zero in math and science, especially in complex analysis and electrical engineering. A complex number can have a zero real part and a non-zero imaginary part. The real part of a complex number affects its position on the complex plane, with a zero real part resulting in the number being located on the imaginary axis.

## Homework Statement

(z+1)^100=(z-1)^100 z is complex

## The Attempt at a Solution

(z-1)/(z+1)=e^(i2pi(k/100))

Now use exp(ix)=cosx+isinx and multiply by the complex conjugate of the denominator.

Word. I think I was just tired. I feel dumb for not seeing that.

## What does it mean for the real part to be zero?

When the real part is zero, it means that the complex number is purely imaginary. This means that the number can be expressed as a multiple of the imaginary unit, i, without any real number component.

## How can you show that the real part is zero?

To show that the real part is zero, you can use the complex conjugate to eliminate the real part. This involves changing the sign of the imaginary component and adding it to the original number. If the resulting number has a zero real part, then the original number also has a zero real part.

## Why is it important to show that the real part is zero?

Showing that the real part is zero is important in many areas of mathematics and science, particularly in complex analysis and electrical engineering. It allows for simpler calculations and can reveal important properties of a complex number or system.

## Can a complex number have a zero real part and non-zero imaginary part?

Yes, a complex number can have a zero real part and a non-zero imaginary part. This means that the number is purely imaginary and can be expressed as a multiple of the imaginary unit, i. An example of this is the number 2i, which has a zero real part and a non-zero imaginary part of 2.

## How does the real part affect the graph of a complex number?

The real part of a complex number determines the horizontal position of the number on the complex plane. When the real part is zero, the number is located on the imaginary axis. This means that the graph of the number will be a point on the imaginary axis instead of a point in the complex plane.