Quiz about Understanding Complex and Polar Forms Quiz

Question 1

What is the modulus of the complex number $$-5 + 5i$$ in polar form?

Accepted Answer

$$5\sqrt{2}$$

Answer

$$10$$

Answer

$$5$$

Answer

$$\sqrt{50}$$

Question 2

What is the argument of the complex number $$1 - i$$ in radians?

Accepted Answer

$$-\frac{\pi}{4}$$

Answer

$$\frac{\pi}{4}$$

Answer

$$\frac{3\pi}{4}$$

Answer

$$-\frac{3\pi}{4}$$

Question 3

What is the modulus of the complex number $$8i$$ in polar form?

Accepted Answer

$$8$$

Answer

$$0$$

Answer

$$64$$

Answer

$$4$$

Question 4

What is the argument of the complex number $$-4 - 4i$$ in radians?

Accepted Answer

$$\frac{3\pi}{4}$$

Answer

$$\frac{5\pi}{4}$$

Answer

$$\frac{7\pi}{4}$$

Answer

$$-\frac{\pi}{4}$$

Question 5

Convert the complex number $$0 - 2i$$ into polar form.

Accepted Answer

$$2(\cos(\frac{3\pi}{2}) + i\sin(\frac{3\pi}{2}))$$

Answer

$$2(\cos(\frac{\pi}{2}) + i\sin(\frac{\pi}{2}))$$

Answer

$$2(\cos(\pi) + i\sin(\pi))$$

Answer

$$2(\cos(0) + i\sin(0))$$

Question 6

Convert the polar form $$4(\cos(\frac{3\pi}{4}) + i\sin(\frac{3\pi}{4}))$$ into complex form.

Accepted Answer

$$-2\sqrt{2} + 2\sqrt{2}i$$

Answer

$$2\sqrt{2} - 2\sqrt{2}i$$

Answer

$$2\sqrt{2} + 2\sqrt{2}i$$

Answer

$$-2\sqrt{2} - 2\sqrt{2}i$$

Question 7

What is the modulus of the complex number $$-3i$$ in polar form?

Accepted Answer

$$3$$

Answer

$$-3$$

Answer

$$9$$

Answer

$$0$$

Question 8

What is the argument of the complex number $$-1$$ in radians?

Accepted Answer

$$\pi$$

Answer

$$-\pi$$

Answer

$$\frac{\pi}{2}$$

Answer

$$-\frac{\pi}{2}$$

Question 9

Convert the complex number $$-6 + 6i$$ into polar form.

Accepted Answer

$$6\sqrt{2}(\cos(\frac{3\pi}{4}) + i\sin(\frac{3\pi}{4}))$$

Answer

$$6\sqrt{2}(\cos(\frac{\pi}{4}) + i\sin(\frac{\pi}{4}))$$

Answer

$$12(\cos(\frac{3\pi}{4}) + i\sin(\frac{3\pi}{4}))$$

Answer

$$6(\cos(\frac{3\pi}{4}) + i\sin(\frac{3\pi}{4}))$$

Question 10

What is the modulus of the complex number $$12 - 5i$$ in polar form?

Accepted Answer

$$13$$

Answer

$$17$$

Answer

$$\sqrt{144 + 25}$$

Answer

$$12$$

Question 11

What is the argument of the complex number $$-7$$ in radians?

Accepted Answer

$$\pi$$

Answer

$$-\pi$$

Answer

$$\frac{\pi}{2}$$

Answer

$$0$$

Question 12

Convert the polar form $$10(\cos(\frac{\pi}{2}) + i\sin(\frac{\pi}{2}))$$ into complex form.

Accepted Answer

$$10i$$

Answer

$$10$$

Answer

$$-10i$$

Answer

$$-10$$

Question 13

What is the modulus of the complex number $$1 + \sqrt{3}i$$ in polar form?

Accepted Answer

$$2$$

Answer

$$\sqrt{3}$$

Answer

$$4$$

Answer

$$\sqrt{4}$$

Understanding Complex and Polar Forms Quiz

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