Polar Form of Complex Numbers

Find the modulus of the complex number. Also state which quadrant the point lies in.

-3 + i

• √10, Quadrant 2

• √10, Quadrant 3

• 2, Quadrant 2

• 3, Quadrant 3

Express this complex number in rectangular form.

4 ( cos π /3 + i sin π /3)

• 2 + 2√3 i

• 2 + √3 i

• 2 - 2√3 i

• -2 + 2√3 i

Express the complex number in polar form.
-2 + 5i

• 5.39 ( cos 1.95 + i sin 1.95)
• 5.39 ( cos 65.06 + i sin 65.06)
• 2.65 ( cos 1.95 - i sin 1.95 )
• 2.65 ( cos 65. 06 - i sin 65.06 )

What complex number is represented by the graph?

• -3-i
• -3+i
• 1+3i
• 1-3i

Find the absolute value of the complex number. Also state the quadrant in which the point lies.

2 + 3i

• √13, Quadrant 1

• √5, Quadrant 1

• √11, Quadrant 2

• √11, Quadrant 3

Express the complex number in polar form.
6 + 2i

• 6.32 ( cos 0.32 + i sin 0.32)
• 6.32 ( cos 0.45 + i sin 0.45)
• 1.73 ( cos 0.32 + i sin 0.32)
• 1.73 ( cos 0.45 - i sin 0.45)

What quadrant would the point in polar form land in?
4 ( cos π /3 + i sin π /3)

• Quadrant 4
• Quadrant 1
• Quadrant 2
• Quadrant 3

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 
(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 product z₁z₂

• -7√3 - 7i

• -7√2 - 7√2i

• -7√2 + 7√2i

• -7 - 7√3i