MATH 122
DeMOIVRE'S THEOREM

1. Find the fourth roots of -1. Give answers in a + bi form.

2. Find the fifth roots of 32. Give answers in trig form.

3. Find the third roots of i. Give answers in a + bi form.

4. Find the third roots of -4 + i. Give answers in trig form.

5. Find the square roots of 1 + i. Give answers in trig form.

6. Find the square roots of 3 - 4i. Give answers in trig form.

 

ANSWERS

1.  cis 45 = i

    cis 135 = i

    cis 225 = i

         cis 315 = i

 

2.  2 cis 0

    2 cis 72

    2 cis 144

    2 cis 216

    2 cis 288

 

3.  cis 30 = i

    cis 150 = - i

    cis 270 = -1

 

4.  2 cis 40

    2 cis 160

    2 cis 280

 

5.  cis 22.5

    cis 202.5

 

6.  cis (-26.6)

    cis (153.4)