Test Objectives
• Demonstrate the ability to simplify square roots of negative numbers
• Demonstrate the ability to find complex solutions for quadratic equations
• Demonstrate the ability to perform operations with complex numbers
• Demonstrate the ability to simplify powers of the imaginary unit i
• Demonstrate the ability to plot a complex number on the complex plane
• Demonstrate the ability to find the absolute value of a complex number
Review of Complex Numbers Practice Test:

#1:

Instructions: Simplify each.

$$a)\hspace{.1em}2\sqrt{-125}$$

$$b)\hspace{.1em}{-3}\sqrt{-27}$$

$$c)\hspace{.1em}{-4}\sqrt{-18}$$

#2:

Instructions: Solve each equation.

$$a)\hspace{.1em}8x^2 + 6x=-2$$

$$b)\hspace{.1em}6x^2 - 5x=-2 - x^2$$

$$c)\hspace{.1em}12x^2 + x=7x^2 - 8$$

#3:

Instructions: Simplify each.

$$a)\hspace{.1em}3\sqrt{-12}\cdot 2\sqrt{-15}$$

$$b)\hspace{.1em}\frac{4\sqrt{-12}}{2\sqrt{64}}$$

$$c)\hspace{.1em}(-10 + 5i) - (-2 - 10i)$$

$$d)\hspace{.1em}(1 - 3i) + (8 - 5i)$$

$$e)\hspace{.1em}(6 - 7i)(-3 - 5i)(-8 - 6i)$$

$$f)\hspace{.1em}\frac{9 + 5i}{-11 - 3i}$$

#4:

Instructions: Simplify each.

$$a)\hspace{.1em}i^{367}$$

$$b)\hspace{.1em}i^{-153}$$

$$c)\hspace{.1em}i^{-162}$$

#5:

Instructions: Plot each complex number and find its absolute value.

$$a)\hspace{.1em}{-5}- 4i$$

$$b)\hspace{.1em}8 + 6i$$

$$c)\hspace{.1em}8i$$

Written Solutions:

#1:

Solutions:

$$a)\hspace{.1em}10i\sqrt{5}$$

$$b)\hspace{.1em}{-9i}\sqrt{3}$$

$$c)\hspace{.1em}{-12i}\sqrt{2}$$

#2:

Solutions:

$$a)\hspace{.1em}\left\{-\frac{3}{8}\pm \frac{\sqrt{7}}{8}i\right\}$$

$$b)\hspace{.1em}\left\{\frac{5}{14}\pm \frac{\sqrt{31}}{14}i\right\}$$

$$c)\hspace{.1em}\left\{-\frac{1}{10}\pm \frac{\sqrt{159}}{10}i\right\}$$

#3:

Solutions:

$$a)\hspace{.1em}{-36}\sqrt{5}$$

$$b)\hspace{.1em}\frac{\sqrt{3}}{2}i$$

$$c)\hspace{.1em}{-8}+ 15i$$

$$d)\hspace{.1em}9 - 8i$$

$$e)\hspace{.1em}370 + 390i$$

$$f)\hspace{.1em}-\frac{57}{65}- \frac{14}{65}i$$

#4:

Solutions:

$$a)\hspace{.1em}{-i}$$

$$b)\hspace{.1em}{-i}$$

$$c)\hspace{.1em}{-1}$$

#5:

Solutions:

$$a)\hspace{.1em}|-5 - 4i|=\sqrt{41}$$

$$b)\hspace{.1em}|8 + 6i|=10$$

$$c)\hspace{.1em}|8i|=8$$