Question 1

Which of the following is the standard form of a complex number?

Accepted Answer

$$a + bi$$

Question 2

What is the value of $$i^2$$ where $$i is $$the imaginary unit?

Accepted Answer

$$-1$$

Question 3

Add the complex numbers $$(5 - 2i)$$ and $$(3 + 3i). $$What is the result in standard form?

Accepted Answer

$$8 + i$$

Question 4

Subtract $$(12 - i)$$ from $$(2 + 6i). $$What is the result in standard form?

Accepted Answer

$$-10 + 7i$$

Question 5

Multiply $$7i by$$ $$(2 - 9i). $$What is the result in standard form?

Accepted Answer

$$63 + 14i$$

Question 6

Find the product of $$(5 + 4i)$$ and $$(6 - 7i).$$

Accepted Answer

$$58 - 11i$$

Question 7

What is the complex conjugate of $$a + bi$$?

Accepted Answer

$$a - bi$$

Question 8

What is the product of a complex number and its conjugate, $$(a + bi)(a - bi)$$?

Accepted Answer

$$a^2$$ + $$b^2$$

Question 9

Divide $$\dfrac{5 + 4i}{4 - i}$$ and express the result in standard form.

Accepted Answer

$$\dfrac{16 + 21i}{17}$$

Question 10

What is the principal square root of $$-27$$?

Accepted Answer

$$3i\sqrt{3}$$

Question 11

Simplify $$\sqrt{-27} + \sqrt{-48}.$$

Accepted Answer

$$7i\sqrt{3}$$

Question 12

Expand and simplify $$(-2 - i\sqrt{3})^2$.

Accepted Answer

$$1 + 4i\sqrt{3}$$

Question 13

Which of the following best describes the process for dividing complex numbers?

Accepted Answer

Multiply numerator and denominator by the conjugate of the denominator

Question 14

A medical engineer is analyzing an electrical circuit with impedance $$Z = 3 + 4i$$ ohms. What is the conjugate of the impedance?

Accepted Answer

$$3 - 4i$$

Question 15

If $$z = 2 - 5i$$, what is $$z \cdot \overline{z}$$, where $$\overline{z} is $$the conjugate of $$z$$?

Accepted Answer

$$29$$

Question 16

Which of the following is NOT a property of complex numbers?

Accepted Answer

The sum of two imaginary numbers is always imaginary

Complex Numbers: Operations and Properties

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