# Section 2.4 – Complex Numbers

Section Details.
• Definition of complex numbers and the real and imaginary parts
• The conjugate of a complex number
• Operations with Complex Numbers

### Practice Problems

Directions. The following are review problems for the section. We recommend you work the problems yourself, and then click "Answer" to check your answer. If you do not understand a problem, you can click "Video" to learn how to solve it.
Consider the complex numbers $$z_1=4+\sqrt{-18}$$ and $$z_2=2+\sqrt{-50}$$.

1. ​Write $$z_1$$ and $$z_2$$ in standard form.

$$z_1=4+3\sqrt{2}i$$
$$z_2=2+5\sqrt{2}i$$

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2. Find $$z_1+z_2$$, $$z_1-z_2$$, and $$z_1z_2$$

$$z_1+z_2=6+8\sqrt{2}i$$,
$$z_1-z_2=2-2\sqrt{2}i$$
$$z_1\cdot z_2=-22+26\sqrt{2}i$$

Video Errata: On $$z_1+z_2$$, $$3\sqrt{2}+5\sqrt{2}=8\sqrt{2}$$ not 7.

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3. Find the conjugate of $$z_2$$

The conjugate of $$z_2$$ is $$2-5\sqrt{2}i$$

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