Polar Coordinates and Complex Numbers

Convert from polar coordinates, (20, 11π/6) to rectangular coordinates.

• (-10√3, 10)

• (10√3, -10)

• (10, -10√3)

• (10√2, -10)

Find the rectangular coordinates of each polar point. (4, 3π/2)

• (4,4)

• (4,0)

• (0,-4)

• (0,1)

Find polar coordinates for the point:
(√3 , 1)

• (2, π/6)

• (-2, -π/6)

• (1,0)

• (4π,-2)

Convert from rectangular to polar coordinates. (-4, 4)

• (4√2, π/4)

• (4√2, 3π/4)

• (4√2, -π/4)

• (-4√2, -7π/4)

What complex number is shown on the graph?

• (-2,-3)

Answer explanation

Since complex numbers can be graphed like rectangular coordinates in a complex plane, converting them to polar form is just like converting rectangular coordinates to polar form.

Write the complex number in polar form

• √50 (cos π/2 + i sin π/2)

• 50 (cos π/4 + i sin π/4)

• √50 (cos 5π/4 + i sin 5π/4)

• √50 (cos π/4 + i sin π/4)

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

Graph R(-3, -145°).

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• (5, -30°)

• (5, 330°)

• (5, -240°)

• (5, -120°)

Graph the polar equation r = 2.5.

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