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
Operations with Complex Numbers Practice Test:

#1:

Instructions: simplify each.

$$a)\hspace{.2em}(3 - 4i) - (-4 - 3i) + 4$$

$$b)\hspace{.2em}(6 + 2i) + 3 + (2 + 6i)$$


#2:

Instructions: simplify each.

$$a)\hspace{.2em}(-8i) - (2 + 6i) + (5 + 7i)$$

$$b)\hspace{.2em}(-4i)(-7i)(8i)$$


#3:

Instructions: simplify each.

$$a)\hspace{.2em}(-6i)(-1 - 6i)$$

$$b)\hspace{.2em}(-2 - 5i)(-2 + 8i)$$


#4:

Instructions: simplify each.

$$a)\hspace{.2em}(7i)(-4 + 7i)(7 - 2i)$$

$$b)\hspace{.2em}-\frac{2}{8i}$$


#5:

Instructions: simplify each.

$$a)\hspace{.2em}\frac{3}{2 + 4i}$$

$$b)\hspace{.2em}\frac{-4 - 8i}{6 + 4i}$$


Written Solutions:

#1:

Solutions:

$$a)\hspace{.2em}11 - i$$

$$b)\hspace{.2em}11 + 8i$$


#2:

Solutions:

$$a)\hspace{.2em}3 - 7i$$

$$b)\hspace{.2em}-224i$$


#3:

Solutions:

$$a)\hspace{.2em}-36 + 6i$$

$$b)\hspace{.2em}44 - 6i$$


#4:

Solutions:

$$a)\hspace{.2em}-399 - 98i$$

$$b)\hspace{.2em}\frac{i}{4}$$


#5:

Solutions:

$$a)\hspace{.2em}\frac{3 - 6i}{10}$$

$$b)\hspace{.2em}\frac{-14 - 8i}{13}$$