Imaginary Numbers Powers

Find 
(3 + 3√3 i )⁴ 
using De Moivre's Theorem and express your answer in rectangular form.

• -648 - 648 √3 i
• -654 - 654 √3 i
• -1962 - 1962 √3 i
• 648 i

Find
 1/2 ( cos π /3 + i sin π /3)
÷ 3 ( cos π /6 + i sin π /6)
and express your final answer in rectangular form.

• √3/12 + 1/12 i
• 12√3 + 12 i
• √3/12 - 1/12 i
• 12√3 - 12i

Find    
5(cos 2π /3 + i sin 2π /3)⋅2( cos π /3 + i sin π /3)
in polar form.  Then express your final answer in rectangular form.

• -10
• 10
• -10i
• 10i

Find the product z₁z₂

• -7√3 - 7i

• -7√2 - 7√2i

• -7√2 + 7√2i

• -7 - 7√3i

Find the quotient z₁ ⁄ z₂

• -3.5 + i
• -3.5i
• -3.5
• 3.5

Find the indicated power using DeMoivre's Theorem 

• 256
• 4096i
• 4096
• -4096

Find the indicated power using DeMoivre's Theorem 

• 72 - 72√3i
• - 72√3 + 72i
• - 72√2 + 72√2i
• -72 + 72√3i

Convert (1 + √3i) to Polar Form.

• 2 (cos(π/6)+isin(π/6))

• 2 (cos(π/3)+isin(π/3))

• 4 (cos(π/6)+isin(π/6))

• 4 (cos(π/3)+isin(π/3))

Find 
(3 + 3√3 i )⁴ 
using De Moivre's Theorem and express your answer in rectangular form.

• -648 - 648 √3 i
• -654 - 654 √3 i
• -1962 - 1962 √3 i
• 648 i

Find the modulus of the complex number. Also state what quadrant the point would land in.

-3 + i

• √10, Quadrant 2

• √10, Quadrant 3

• 2, Quadrant 2

• 3, Quadrant 3