Precalculus with Limits: A Graphing Approach, Sixth Edition
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Precalculus with Limits: A Graphing Approach, Sixth Edition View details
5. Trigonometric Form of a Complex Number
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Exercise 1 Page 452

modulus

We are asked to complete the following statement.

The of a complex number a+bi is the distance between the origin (0,0) and the point (a,b).

First, recall that complex numbers can be represented on a two-dimensional plane known as the complex plane. In this plane, the horizontal axis represents the real part of the complex number, while the vertical axis represents the imaginary part. This allows every complex number to be shown as a point.
Complex plane with points on it

Now, let's find the distance between the origin and an example complex number using the Pythagorean Theorem.

Complex plane with points on it

We found that the distance, which is also called the modulus, is sqrt(2^2+3^2). Let's finish the given statement.

The modulus of a complex number a+bi is the distance between the origin (0,0) and the point (a,b).