Complex Numbers: Powers and Roots

What is the result of multiplying two complex numbers in polar form?

• The difference of their magnitudes and the sum of their angles

• The product of their magnitudes and the difference of their angles

• The sum of their magnitudes and the product of their angles

• The product of their magnitudes and the sum of their angles

According to De Moivre's Theorem, what is (1 - i)^8?

• 8

• 64

• 16

• 32

How many distinct nth roots does a complex number have?

• 2n

• n-1

• n+1

• n

What is the polar form of the complex number i?

• 1 * (cos(0) + i sin(0))

• 1 * (cos(π/4) + i sin(π/4))

• 1 * (cos(π) + i sin(π))

• 1 * (cos(π/2) + i sin(π/2))

What is one of the cube roots of i?

• √3/2 + i/2

• -√3/2 - i/2

• -√3/2 + i/2

• √3/2 - i/2

What is the magnitude of the complex number 2 - 2√3i?

• 2

• 4

• 16

• 8

In which quadrant is the complex number 2 - 2√3i located?

• Quadrant IV

• Quadrant III

• Quadrant II

• Quadrant I

What is the reference angle for the complex number 2 - 2√3i?

• π/4

• π/3

• π/6

• π/2

What is the polar form of the fourth root of 2 - 2√3i when k=0?

• 4√4 * (cos(5π/4) + i sin(5π/4))

• 4√4 * (cos(5π/2) + i sin(5π/2))

• 4√4 * (cos(5π/3) + i sin(5π/3))

• 4√4 * (cos(5π/12) + i sin(5π/12))

What is the rectangular form of the fourth root of 2 - 2√3i when k=0?

• 3.66 + 2.36i

• 2.66 + 2.36i

• 2.66 + 1.36i

• 3.66 + 1.36i