Complex Numbers and the Polar Coordinate Plane

Find the absolute value of the complex number. Also state what quadrant the point would land in.
2 + 3i

• √13,  Quadrant 1
• √5,  Quadrant 1
• √11, Quadrant 2
• √11, Quadrant 3

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

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 class are you in?

• Precalculus
• Algebra 2
• Algebra 1
• P.E

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

Express the point in polar form 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

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
 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 
(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