About Operations with Complex Numbers:
A complex number is of the form: a + bi. In our lesson, we learned about adding complex numbers, subtracting complex numbers, multiplying complex numbers, and dividing complex numbers. We also learned how to rationalize a complex binomial denominator using complex conjugates.
Test Objectives
- Demonstrate the ability to add and subtract complex numbers
- Demonstrate the ability to multiply complex numbers
- Demonstrate the ability to divide complex numbers
- Demonstrate the ability to rationalize a complex binomial denominator
#1:
Instructions: simplify each.
$$a)\hspace{.2em}(3 - 4i) - (-4 - 3i) + 4$$
$$b)\hspace{.2em}(6 + 2i) + 3 + (2 + 6i)$$
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#2:
Instructions: simplify each.
$$a)\hspace{.2em}(-8i) - (2 + 6i) + (5 + 7i)$$
$$b)\hspace{.2em}(-4i)(-7i)(8i)$$
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#3:
Instructions: simplify each.
$$a)\hspace{.2em}(-6i)(-1 - 6i)$$
$$b)\hspace{.2em}(-2 - 5i)(-2 + 8i)$$
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#4:
Instructions: simplify each.
$$a)\hspace{.2em}(7i)(-4 + 7i)(7 - 2i)$$
$$b)\hspace{.2em}{-}\frac{2}{8i}$$
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#5:
Instructions: simplify each.
$$a)\hspace{.2em}\frac{3}{2 + 4i}$$
$$b)\hspace{.2em}\frac{-4 - 8i}{6 + 4i}$$
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Written Solutions:
#1:
Solutions:
$$a)\hspace{.2em}11 - i$$
$$b)\hspace{.2em}11 + 8i$$
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#2:
Solutions:
$$a)\hspace{.2em}3 - 7i$$
$$b)\hspace{.2em}{-}224i$$
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#3:
Solutions:
$$a)\hspace{.2em}{-}36 + 6i$$
$$b)\hspace{.2em}44 - 6i$$
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#4:
Solutions:
$$a)\hspace{.2em}{-}399 - 98i$$
$$b)\hspace{.2em}\frac{i}{4}$$
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#5:
Solutions:
$$a)\hspace{.2em}\frac{3}{10} - \frac{3}{5}i$$
$$b)\hspace{.2em}{-}\frac{14}{13} - \frac{8}{13}i$$
