Question 1

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

Accepted Answer

$$a + bi$$

Question 2

Identify the real and imaginary parts of the complex number $$7 - 4i.$$

Accepted Answer

Real part: $$7$$, Imaginary part: $$-4i$$

Question 3

What is the sum of $$(3 + 2i)$$ and $$(4 - 5i)$$?

Accepted Answer

$$7 - 3i$$

Question 4

Find the difference: $$(2 + 6i) - (4 - i).$$

Accepted Answer

$$-2 + 7i$$

Question 5

Multiply the complex numbers: $$(3 + 2i)(4 - i).$$

Accepted Answer

$$14 + 5i$$

Question 6

What is the product of $$(2 + 3i)$$ and its conjugate?

Accepted Answer

$$13$$

Question 7

Which of the following is the conjugate of $$5 - 2i$$?

Accepted Answer

$$5 + 2i$$

Question 8

Divide $$3 by$$ $$1 + 2i$$ and express your answer in standard form.

Accepted Answer

$$\frac{3(1 - 2i)}{5}$$

Question 9

If $$z = 4 + 3i$$, what is $$z^*$$, the complex conjugate of $$z$$?

Accepted Answer

$$4 - 3i$$

Question 10

Which operation will always result in a real number when performed between a complex number and its conjugate?

Accepted Answer

Multiplication

Question 11

A medical imaging device uses the complex number $$6 - 2i to $$represent a signal. What is the magnitude of this signal?

Accepted Answer

$$\sqrt{40}$$

Question 12

Which of the following is the result of $$(2 + 5i) + (3 - 2i)$$?

Accepted Answer

$$5 + 3i$$

Question 13

A signal in an electrical circuit is represented by $$-7 + 4i. $$What is the conjugate of this signal?

Accepted Answer

$$-7 - 4i$$

Question 14

What is the result of dividing $$-5 + 3i by$$ $$2 - i$$?

Accepted Answer

$$\frac{-7 + 11i}{5}$$

Question 15

Which of the following is the result of multiplying $$(1 + 2i)$$ and $$(3 - i)$$?

Accepted Answer

$$5 + 5i$$

Question 16

If $$z = 2 + 3i$$, what is $$|z|$$, the modulus of $$z$$?

Accepted Answer

$$\sqrt{13}$$

Question 17

A chemical reaction is modeled by the complex number $$4 + 6i. $$What is the sum of this number and its conjugate?

Accepted Answer

$$8$$

Question 18

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

Accepted Answer

The quotient of a complex number and its conjugate is always real.

Question 19

Which of the following is the result of $$(2 + 3i) - (5 - 2i)$$?

Accepted Answer

$$-3 + 5i$$

Question 20

A signal in a communications system is represented by $$x = 8 - 6i. $$What is the product of $$x$$ and its conjugate?

Accepted Answer

$$100$$

Complex Numbers: Definitions, Operations, and Conjugates

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