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Chapter 6: Problem 23

Plot each complex number. Then write the complex number in polar form. You may express the argument in degrees or radians. $$-3+4 i$$

Short Answer

Expert verified
The complex number can be represented on an Argand Diagram at the point (-3,4). The polar form of the given complex number is \(5e^{i(atan2(4,-3))}\).

Step by step solution

01

Plotting the Complex Number

The complex number \(-3+4i\) can be represented as a point in the complex plane (Argand Diagram) with the real part \(-3\) on the x-axis and the imaginary part \(4i\) on the y-axis.
02

Converting the Complex Number to Polar Form

In polar form, a complex number is represented as \(r(e^{i\theta})\) where \(r\) is the magnitude of the complex number and \(\theta\) is the argument. The magnitude, \(r\), can be calculated using Pythagoras' theorem, \(|r| = \sqrt{(-3)^2 + (4)^2} = 5 \). The argument \(\theta\) can be calculated using the formula \(\theta = atan2(imaginary part, real part) = atan2(4,-3)\), this can be calculated either in degrees or radians.

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