Question 1

Write the expression in the standard form $$a + bi$$: $$(2 - 3i) + (9 + 8i)$$

Accepted Answer

$$11 + 5i$$

Question 2

Write the expression in the standard form $$a + bi$$: $$(2 + 7i) - (9 - 3i)$$

Accepted Answer

$$-7 + 10i$$

Question 3

Subtract and simplify your answer in the form $$a + bi$$: $$6 - (8 + 8i) - (-4 - i)$$

Accepted Answer

$$2 - 7i$$

Question 4

Find the product and write the result in standard form: $$9i(5i - 3)$$

Accepted Answer

$$-45i - 27$$

Question 5

Find the following product and write the result in standard form, $$a + bi$$: $$(-7 + 7i)(3 + i)$$

Accepted Answer

$$-28 + 14i$$

Question 6

Multiply and write the answer in the form $$a + bi$$: $$(8 + 9i)(8 - 9i)$$

Accepted Answer

$$145$$

Question 7

Divide and simplify in the form $$a + bi$$: $$\frac{52i}{5 + i}$$

Accepted Answer

$$2 - 10i$$

Question 8

Perform the indicated operation and write the result in standard form: $$\sqrt{-16} - \sqrt{-4}$$

Accepted Answer

$$2i$$

Question 9

Solve for $$x$$ using the quadratic formula: $$x^2 - 4x + 29 = 0$$

Accepted Answer

$$2 \pm 5i$$

Question 10

Perform the indicated operations and write the answer in the form $$a + bi$$: $$(4 - 3i)(1 - i) - (4 - i)(4 + i)$$

Accepted Answer

$$-11 - 7i$$

Question 11

Write the expression in the standard form $$a + bi$$: $$(3 - 9i)(5 + 4i)$$

Accepted Answer

$$51 - 21i$$

Question 12

A certain electrical circuit has an impedance of $$Z = 3 + 4i$$ ohms. What is the magnitude of the impedance?

Accepted Answer

$$5$$ ohms

Question 13

If $$z = 2 - 5i$$ and $$w = 1 + 3i$$, what is $$z \cdot w in $$the form $$a + bi$$?

Accepted Answer

$$17 - 7i$$

Question 14

Which of the following is the conjugate of $$7 - 6i$$?

Accepted Answer

$$7 + 6i$$

Question 15

If $$z = 4 + 3i$$, what is $$\frac{1}{z} in $$the form $$a + bi$$?

Accepted Answer

$$\frac{4}{25} - \frac{3}{25}i$$

Question 16

Which of the following represents the solution to $$x^2 + 1 = 0$?

Accepted Answer

$$x = \pm i$$

Precalculus Complex Numbers and Quadratic Formula Study Guide

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