Question 1

Which of the following is the correct definition of a complex number?

Accepted Answer

$a + bi$, where $a$ and $b$ are real numbers and $i = \sqrt{-1}$

Question 2

What is the value of $i^2$?

Accepted Answer

$-1$

Question 3

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

Accepted Answer

$a + bi$

Question 4

If $z = 3 - 4i$, what is the complex conjugate of $z$?

Accepted Answer

$3 + 4i$

Question 5

Add the complex numbers $(-2 + 5i)$ and $(3 - 4i)$. What is the result in standard form?

Accepted Answer

$1 + i$

Question 6

Subtract $(2 - 3i)$ from $(5 + 2i)$. What is the result?

Accepted Answer

$3 + 5i$

Question 7

Multiply $(2 + 3i)$ and $(1 - 4i)$. What is the result in standard form?

Accepted Answer

$14 - 5i$

Question 8

Divide $8 - 12i$ by $5 + 4i$ and write the result in standard form.

Accepted Answer

$\frac{8 - 12i}{5 + 4i} = \frac{8 \cdot 5 + 8 \cdot 4i - 12i \cdot 5 - 12i \cdot 4i}{(5 + 4i)(5 - 4i)} = \frac{76 - 68i}{41} = \frac{76}{41} - \frac{68}{41}i$

Question 9

Which of the following statements is TRUE about the real and imaginary parts of a complex number $a + bi$?

Accepted Answer

$a$ is the real part and $b$ is the imaginary part

Question 10

A medical imaging device uses the number $4 - 3i$ to represent a signal. If the device receives a signal $2 + 5i$ at the same time, what is the sum of the two signals?

Accepted Answer

$6 + 2i$

Question 11

If $i = \sqrt{-1}$, what is the value of $i^4$?

Accepted Answer

$1$

Question 12

Which of the following is NOT a complex number?

Accepted Answer

$\sqrt{2}$

Question 13

A chemical reaction is modeled by the equation $z = 2 + 3i$. What is the result if the reaction is reversed, represented by the conjugate of $z$?

Accepted Answer

$2 - 3i$

Question 14

Which operation is performed first when multiplying two complex numbers $(a + bi)(c + di)$?

Accepted Answer

Multiply $a$ by $c$

Question 15

If $z_1 = 1 + 2i$ and $z_2 = 3 - i$, what is $z_1 \cdot z_2$?

Accepted Answer

$5 + 5i$

Question 16

Divide $6 + 8i$ by $2 - i$ and write the result in standard form.

Accepted Answer

$4 + 4i$

Question 17

Which of the following best describes the imaginary unit $i$?

Accepted Answer

$i$ is defined as $\sqrt{-1}$

Question 18

A physicist models a wave using the complex number $5i$. What is the real part of this number?

Accepted Answer

$0$

Complex Numbers: Definitions, Operations, and Examples

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