Graphing Complex Numbers Quiz 1

Question 1

Convert the given complex number to polar form: $$-2$$.

Accepted Answer

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

Answer

$$2\left( \cos \dfrac{\pi }{2}+i\sin \dfrac{\pi }{2} \right)$$

Answer

$$-2\left( \cos \pi +i\sin \pi  \right)$$

Answer

$$2\left( \cos \left( -\pi  \right)+i\sin \left( -\pi  \right) \right)$$

Question 2

Convert the given complex number to polar form: $$-i$$

Accepted Answer

$$1\left( \cos \left( \dfrac{-\pi }{2} \right)+i\sin \left( \dfrac{-\pi }{2} \right) \right)$$

Answer

$$1\left( \cos \left( \dfrac{-\pi }{3} \right)+i\sin \left( \dfrac{-\pi }{3} \right) \right)$$

Answer

$$1\left( \cos \left( \dfrac{-2\pi }{3} \right)+i\sin \left( \dfrac{-2\pi }{3} \right) \right)$$

Answer

$$1\left( \cos \left( \dfrac{\pi }{2} \right)+i\sin \left( \dfrac{\pi }{2} \right) \right)$$

Question 3

Find the modulus and the argument of the complex number $$z=1-\sqrt{3}i$$.

Accepted Answer

2 and $$\dfrac{-\pi }{3}$$

Answer

2 and $$\dfrac{-2\pi }{3}$$

Answer

3 and $$\dfrac{-\pi }{2}$$

Answer

2 and $$\dfrac{-3\pi }{2}$$

Question 4

Represent the complex number $$z=-1+\sqrt{3}i$$ in the polar form.

Accepted Answer

$$2\left( \cos \dfrac{2\pi }{3}+i\sin \dfrac{2\pi }{3} \right)$$

Answer

$$2\left( \cos \dfrac{\pi }{3}+i\sin \dfrac{\pi }{3} \right)$$

Answer

$$2\left( \cos \dfrac{3\pi }{2}+i\sin \dfrac{3\pi }{2} \right)$$

Answer

$$2\left( \cos \dfrac{-\pi }{3}+i\sin \dfrac{-\pi }{3} \right)$$

Question 5

Represent the complex number $$z=\sin \dfrac{2\pi }{3}-i\cos \dfrac{2\pi }{3}$$in the polar form.

Accepted Answer

$$1\left( \cos \dfrac{\pi }{6}+i\sin \dfrac{\pi }{6} \right)$$

Answer

$$1\left( \cos \dfrac{\pi }{3}+i\sin \dfrac{\pi }{3} \right)$$

Answer

$$2\left( \cos \dfrac{\pi }{6}+i\sin \dfrac{\pi }{6} \right)$$

Answer

$$1\left( \cos \dfrac{\pi }{2}+i\sin \dfrac{\pi }{2} \right)$$