What is the angle of a complex number with a coefficient of i?

In summary, the conversation discusses two complex numbers, A and B, where A=2exp[-ikz] and B=2iexp[-ikz]. The speaker is trying to find the angle of these numbers, specifically for B, but is unsure due to the presence of the imaginary number i. The hint given is i=ei(something), and the solution is found to be i=e^{\frac{\pi i}{2}}.
  • #1
roz77
16
0
I have two complex numbers, let's call them A and B. A=2exp[-ikz], and B=2iexp[-ikz]. I have to figure out the angle of these two numbers, and I am just completely drawing a blank on B. I know that the angle of A is just -kz, but I can't remember how to figure it out for part B. I can't remember what that i in front does.
 
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  • #2
hi roz77! :smile:

hint: i = ei(what?) :wink:
 
  • #3
k and z are just random variables that were in the problem. I know that when its exp[ikz], the angle is kz, but I'm not sure when it's iexp[ikz].
 
  • #4
no, i mean solve i = ei(something) :smile:
 
  • #5
[tex]
i=e^{\frac{\pi i}{2}}
[/tex]
 

What is the definition of a complex number angle?

A complex number angle is a measure of rotation or direction in the complex plane. It is represented by the argument of a complex number, which is the angle between the positive real axis and the vector representing the complex number.

How do I find the angle of a complex number?

The angle of a complex number can be found by taking the inverse tangent of the imaginary part divided by the real part. This can be represented as θ = tan-1(Im(z)/Re(z)), where z is the complex number and θ is the angle in radians.

Can the angle of a complex number be negative?

Yes, the angle of a complex number can be negative. A negative angle indicates a rotation in the clockwise direction, while a positive angle indicates a rotation in the counterclockwise direction.

What is the range of complex number angles?

The range of complex number angles is from -π to π radians. This is because the complex number plane is circular, and one full rotation corresponds to 2π radians. Therefore, any angle outside of this range can be simplified to an equivalent angle within this range.

How are complex number angles used in mathematics and science?

Complex number angles are used in various fields of mathematics and science, including physics, engineering, and signal processing. They are particularly useful in analyzing and solving problems involving oscillatory functions, such as waves and vibrations, as well as in representing and manipulating complex numbers in polar form.

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