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Exercises Trigonometry

Example 3 from Algebra and Trigonometry, 10.5 Polar Form of Complex Numbers

Finding the Absolute Value of a Complex Number

Given $z = 3 - 4 i,$ find $| z | .$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
Using the formula, we have
$\begin{array}{l} | z | = \sqrt{x^{2} + y^{2}} \\ | z | = \sqrt{{(3)}^{2} + {(- 4)}^{2}} \\ | z | = \sqrt{9 + 16} \\ \begin{array}{l} | z | = \sqrt{25} \\ | z | = 5 \end{array} \end{array}$
The absolute value $z$ is 5. See Figure 4.

Figure 4

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Given $z = 1 - 7 i,$ find $| z | .$

How did it go?

PreviousFinding the Absolute Value of a Complex Number with a Radical Next Expressing a Complex Number Using Polar Coordinates

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 10.5, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.