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

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

Step-by-step 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)

step-by-step explanation:

at each of the parallel lines adjacent angles are supplementary. the angles have special names identifying their positions with respect to the parallel lines and transversal. they are corresponding angles, alternate interior angles, or alternate exterior angles. an angles is congruent to its matched angle.