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Homework Statement
(z+1)^100=(z-1)^100 z is complex
Homework Equations
The Attempt at a Solution
(z-1)/(z+1)=e^(i2pi(k/100))
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.
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.
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.
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.
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.