Question

Convert -√3-i to polar form.

a. 2cis(pi)/6
b. 2cis5(pi)/6
c. 2cis7(pi)/6
d. 2cis11(pi)/6
e. 2cis4(pi)/6

Answer 1

c

Explanation:

it just is

Answer 2

-sqrt(3) -i = 2 cis (7pi/6)

Explanation:

-sqrt(3) -i

We can find the radius

r = sqrt( (-sqrt(3)) ^2 + (-1) ^2)

= sqrt( 3 + 1)

= sqrt(4)

= 2

theta = arctan (y/x)

arctan (-1/-sqrt(3))

arctan (1/sqrt(3))

theta = pi/6

But this is in the first quadrant, and we need it in the third quadrant

Add pi to move it to the third quadrant

theta = pi/6 + 6pi/6

=7pi/6

-sqrt(3) -i = 2 cis (7pi/6)