- 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
#1:
Instructions: Simplify each.
$$a)\hspace{.1em}2\sqrt{-125}$$
$$b)\hspace{.1em}{-3}\sqrt{-27}$$
$$c)\hspace{.1em}{-4}\sqrt{-18}$$
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#2:
Instructions: Solve each equation.
$$a)\hspace{.1em}8x^2 + 6x=-2$$
$$b)\hspace{.1em}6x^2 - 5x=-2 - x^2$$
$$c)\hspace{.1em}12x^2 + x=7x^2 - 8$$
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#3:
Instructions: Simplify each.
$$a)\hspace{.1em}3\sqrt{-12}\cdot 2\sqrt{-15}$$
$$b)\hspace{.1em}\frac{4\sqrt{-12}}{2\sqrt{64}}$$
$$c)\hspace{.1em}(-10 + 5i) - (-2 - 10i)$$
$$d)\hspace{.1em}(1 - 3i) + (8 - 5i)$$
$$e)\hspace{.1em}(6 - 7i)(-3 - 5i)(-8 - 6i)$$
$$f)\hspace{.1em}\frac{9 + 5i}{-11 - 3i}$$
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#4:
Instructions: Simplify each.
$$a)\hspace{.1em}i^{367}$$
$$b)\hspace{.1em}i^{-153}$$
$$c)\hspace{.1em}i^{-162}$$
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#5:
Instructions: Plot each complex number and find its absolute value.
$$a)\hspace{.1em}{-5}- 4i$$
$$b)\hspace{.1em}8 + 6i$$
$$c)\hspace{.1em}8i$$
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Written Solutions:
#1:
Solutions:
$$a)\hspace{.1em}10i\sqrt{5}$$
$$b)\hspace{.1em}{-9i}\sqrt{3}$$
$$c)\hspace{.1em}{-12i}\sqrt{2}$$
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#2:
Solutions:
$$a)\hspace{.1em}\left\{-\frac{3}{8}\pm \frac{\sqrt{7}}{8}i\right\}$$
$$b)\hspace{.1em}\left\{\frac{5}{14}\pm \frac{\sqrt{31}}{14}i\right\}$$
$$c)\hspace{.1em}\left\{-\frac{1}{10}\pm \frac{\sqrt{159}}{10}i\right\}$$
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#3:
Solutions:
$$a)\hspace{.1em}{-36}\sqrt{5}$$
$$b)\hspace{.1em}\frac{\sqrt{3}}{2}i$$
$$c)\hspace{.1em}{-8}+ 15i$$
$$d)\hspace{.1em}9 - 8i$$
$$e)\hspace{.1em}370 + 390i$$
$$f)\hspace{.1em}-\frac{57}{65}- \frac{14}{65}i$$
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#4:
Solutions:
$$a)\hspace{.1em}{-i}$$
$$b)\hspace{.1em}{-i}$$
$$c)\hspace{.1em}{-1}$$
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#5:
Solutions:
$$a)\hspace{.1em}|-5 - 4i|=\sqrt{41}$$ 
$$b)\hspace{.1em}|8 + 6i|=10$$ 
$$c)\hspace{.1em}|8i|=8$$ 
