What is the angle of a complex number?

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SUMMARY

The angle of a complex number, referred to as its "argument," is determined using the formula tan(θ) = Im(z) / Re(z). For the complex number z = 6 - 5i, the real part is 6 and the imaginary part is -5. This results in an angle that can be calculated using the arctangent function, specifically θ = arctan(-5/6). Understanding this concept is essential for working with complex numbers in mathematics and engineering.

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  • Understanding of complex numbers and their components (real and imaginary parts).
  • Familiarity with trigonometric functions, particularly tangent and arctangent.
  • Basic knowledge of the complex plane and its geometric interpretation.
  • Ability to perform calculations involving angles and radians.
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  • Study the geometric representation of complex numbers in the complex plane.
  • Learn how to convert complex numbers from rectangular to polar form.
  • Explore the properties of complex number multiplication and division.
  • Investigate applications of complex numbers in electrical engineering and signal processing.
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Students, mathematicians, and engineers who are working with complex numbers, particularly those involved in fields such as electrical engineering, physics, and applied mathematics.

l2udolph
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Help me please. I'm not sure how to do this.. Can you tell me about imaginary numbers?
I'm supposed to calculate the angle of z=6-5i
How do I do this?
 
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l2udolph said:
Help me please. I'm not sure how to do this.. Can you tell me about imaginary numbers?
I'm supposed to calculate the angle of z=6-5i
How do I do this?

Actually, that is a complex number, with real and imaginary parts. This article should help you figure out how to find the angle between the complex number vector and the x-axis:

http://en.wikipedia.org/wiki/Complex_numbers

.
 
The "angle" of a complex number, z, more commonly called its "argument", is the angle the line from 0 to z, in the complex plane, makes with the positive real axis.
tan(\theta)= \frac{Im(z)}{Re(z)}
 

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