$$\tan$$^{-1}$$\left(\frac{5}{2}\right)$$

$$\tan$$^{-1}$$\left(\frac{4}{3}\right)$$

Question 1

Given the complex numbers $$z_1 = 4 + 3i$ and z_2$ = 2 - 5i$$, what is $$z_1$$ + $$z_2 in $$standard $$a + bi$$ form?

Accepted Answer

$$6 - 2i$$

Question 2

If $$z = 6 - 2i$$, what is the conjugate of $$z$$?

Accepted Answer

$$6 + 2i$$

Question 3

Which of the following is the result of multiplying $$(3 + 4i)$$ and $$(2 - i)$$?

Accepted Answer

$$10 + 5i$$

Question 4

A medical imaging device uses the complex number $$z = 5 + 12i to $$represent a signal. What is the modulus of $$z$$?

Accepted Answer

$$13$$

Question 5

Simplify the expression $$(2 + 3i) - (5 - 2i)$$ and write the result in $$a + bi$$ form.

Accepted Answer

$$-3 + 5i$$

Question 6

A chemical reaction is modeled by the complex number $$z = 7 - 4i. $$What is the real part of $$z$$?

Accepted Answer

$$7$$

Question 7

Which of the following is the result of dividing $$(8 + 6i) by$$ $$(2 + i)$$? Express your answer in $$a + bi$$ form.

Accepted Answer

$$4 + 2i$$

Question 8

If $$z = 3 - 7i$$, what is $$z^*$$, the complex conjugate of $$z$$?

Accepted Answer

$$3 + 7i$$

Question 9

A signal in an electrical circuit is represented by $$z = 2 + 5i. $$What is the argument (angle) of $$z in $$radians?

Accepted Answer

$$	an$$^{-1}$$\left(\frac{5}{2}ight)$$

Question 10

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

Accepted Answer

$$5 + i$$

Question 11

A historical event is modeled by the complex number $$z = -2 + 6i. $$What is the modulus of $$z$$?

Accepted Answer

$$\sqrt{40}$$

Question 12

Simplify $$(4 - 3i) + (7 + 2i)$$ and write the result in $$a + bi$$ form.

Accepted Answer

$$11 - i$$

Question 13

If $$z_1 = 5 + 2i$ and z_2$ = 3 - 4i$$, what is $$z_1$$ - $$z_2$$?

Accepted Answer

$$2 + 6i$$

Question 14

A real-world application uses the complex number $$z = 0 + 8i. $$What is the modulus of $$z$$?

Accepted Answer

$$8$$

Question 15

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

Accepted Answer

$$13$$

Question 16

If $$z = 7 + 24i$$, what is the modulus of $$z$$?

Accepted Answer

$$25$$

Question 17

A signal is represented by $$z = 3 + 4i. $$What is the argument of $$z in $$radians?

Accepted Answer

$$	an$$^{-1}$$\left(\frac{4}{3}ight)$$

Question 18

Simplify $$(5 + 2i) + (3 - 7i)$$ and write the result in $$a + bi$$ form.

Accepted Answer

$$8 - 5i$$

Question 19

If $$z = 6 - 8i$$, what is the modulus of $$z$$?

Accepted Answer

$$10$$

Question 20

Which of the following is the result of dividing $$(3 + 4i) by$$ $$(1 - 2i)$$? Express your answer in $$a + bi$$ form.

Accepted Answer

$$-1 + 2i$$

Complex Numbers: Operations and Standard Form

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