## Trigonometry (11th Edition) Clone

Published by Pearson

# Chapter 8 - Complex Numbers, Polar Equations, and Parametric Equations - Section 8.1 Complex Numbers - 8.1 Exercises - Page 364: 96

#### Answer

The solution set of this problem, written in standard form, is $$\Big\{1\pm i\Big\}$$

#### Work Step by Step

$$x^2+2=2x$$ The equation is not in standard form, so first, we need to bring it back to standard form: $$x^2-2x+2=0$$ Now the equation is in standard form, the quadratic formula can be applied. $$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$ As $a=1, b=-2, c=2$ $$x=\frac{-(-2)\pm\sqrt{(-2)^2-4\times1\times2}}{2\times1}$$ $$x=\frac{2\pm\sqrt{4-8}}{2}$$ $$x=\frac{2\pm\sqrt{-4}}{2}$$ Now we rewrite $\sqrt{-4}=i\sqrt{4}=2i$ $$x=\frac{2\pm 2i}{2}$$ Finally, we simplify $$x=1\pm i$$ The solution set of this problem, written in standard form, is $$\Big\{1\pm i\Big\}$$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.