Question 1

Given $$z_1 = 2$$ \operatorname{cis} 30^\circ$$ and z_2$ = 3 \operatorname{cis} 45^\circ$$, what is the product $$z_1$$ $$z_2 in $$polar form?

Accepted Answer

$$6 \operatorname{cis} 75^\circ$$

Question 2

If $$z_1 = 4$$ \operatorname{cis} 120^\circ$$ and z_2$ = 2 \operatorname{cis} 60^\circ$$, what is $$\dfrac{z_1$}{z_2$} in $$polar form?

Accepted Answer

$$2 \operatorname{cis} 60^\circ$$

Question 3

Let $$z_1 = 5$$ \operatorname{cis} 45^\circ$$ and z_2$ = 2 \operatorname{cis} 120^\circ. $$Find the argument of $$z_1$$ $$z_2.$$

Accepted Answer

$$165^\circ$$

Question 4

If $$z_1 = 3$$ \operatorname{cis} 210^\circ$$ and z_2$ = 4 \operatorname{cis} 330^\circ$$, what is the modulus of $$z_1$$ $$z_2$$?

Accepted Answer

$$12$$

Question 5

Given $$z_1 = 6$$ \operatorname{cis} 90^\circ$$ and z_2$ = 2 \operatorname{cis} 45^\circ$$, what is the argument of $$\dfrac{z_1$}{z_2$}$$?

Accepted Answer

$$45^\circ$$

Question 6

If $$z_1$$ = $$r_1$$ \operatorname{cis} \$$theta_1$$ and $$z_2$$ = $$r_2$$ \operatorname{cis} \$$theta_2$$, which of the following correctly expresses $$z_1$$ $$z_2$$?

Accepted Answer

$$r_1$$ $$r_2$$ \operatorname{cis} (\$$theta_1$$ + \$$theta_2$$)$$

Question 7

Suppose $$z_1 = 7$$ \operatorname{cis} 10^\circ$$ and z_2$ = 2 \operatorname{cis} 350^\circ. $$What is the argument of $$z_1$$ $$z_2$$?

Accepted Answer

$$0^\circ$$

Question 8

If $$z_1 = 8$$ \operatorname{cis} 270^\circ$$ and z_2$ = 2 \operatorname{cis} 90^\circ$$, what is $$z_1$$ $$z_2$$?

Accepted Answer

$$16 \operatorname{cis} 0^\circ$$

Question 9

Given $$z_1 = 5$$ \operatorname{cis} 60^\circ$$ and z_2$ = 5 \operatorname{cis} 120^\circ$$, what is $$\dfrac{z_1$}{z_2$}$$?

Accepted Answer

$$1 \operatorname{cis} (-60^\circ)$$

Question 10

If $$z_1 = 10$$ \operatorname{cis} 45^\circ$$ and z_2$ = 2 \operatorname{cis} 15^\circ$$, what is the modulus of $$\dfrac{z_1$}{z_2$}$$?

Accepted Answer

$$5$$

Question 11

A voltage in an AC circuit is represented as $$V = 120 \operatorname{cis} 30^\circ$$ volts and the current as $$I = 10 \operatorname{cis} -15^\circ$$ amperes. What is the phase difference between voltage and current?

Accepted Answer

$$45^\circ$$

Question 12

If $$z_1 = 3$$ \operatorname{cis} 80^\circ$$ and z_2$ = 4 \operatorname{cis} 100^\circ$$, what is the argument of $$\dfrac{z_1$}{z_2$}$$?

Accepted Answer

$$-20^\circ$$

Question 13

Given $$z_1 = 2$$ \operatorname{cis} 0^\circ$$ and z_2$ = 2 \operatorname{cis} 180^\circ$$, what is $$z_1$$ $$z_2$$?

Accepted Answer

$$4 \operatorname{cis} 180^\circ$$

Question 14

If $$z_1 = 1$$ \operatorname{cis} 270^\circ$$ and z_2$ = 1 \operatorname{cis} 90^\circ$$, what is $$z_1$$ $$z_2$$?

Accepted Answer

$$1 \operatorname{cis} 0^\circ$$

Question 15

Let $$z_1 = 2$$ \operatorname{cis} 45^\circ$$ and z_2$ = 3 \operatorname{cis} 135^\circ. $$What is the modulus of $$z_1$$ $$z_2$$?

Accepted Answer

$$6$$

Products and Roots of Complex Numbers in Trigonometric Form

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