apex-highprecalc-10112-6-3-practice-complex-numbers

12.6.3 Practice: Complex Numbers Practice



Answer the following questions using what you've learned from this unit. Write your responses in the space
provided.



For questions 1 - 3, the polar coordinates of a point are given. Find the rectangular coordinates of each point. (2
points each)




1.

X = rcos ø = 2 cos 3pi/4 = 2 cos pi/2 + pi/4 = -2 sin pi/4 = -2(1/−√2) = -−√2
Y = rsinø = 2 sin 3pi/4 = 2 sin pi/2 + pi/4 = 2 cos pi/4 = 2(1/√2) = √2

(-√2, √2)




2.

X = rcosø = -4cos 7pi/6 = -4cos (pi + pi/6) = -4(-cos pi/6) = 4cospi/6 = 4(√3/2) = 2√3
Y = rinsinø = -4 sin 7pi/6 = -4sin (pi + pi/6) = -4(-sin pi/6) = 4sinpi/6 = 4 (½) = 2



( 2√3, 2)




3.

X = rcosø =2/3cos (-2pi/3) = ⅔(-½) = -⅓
Y = rsinø = 2/3sin (-2pi/3) =⅔ (-√3/2) = -√3/3



( -⅓, -√3/3)




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, For questions 4 - 6, the rectangular coordinates of a point are given. Find the polar coordinates of each point. (2
points each)



4. (4, 0)




5. (3, 4)




6. (2, -2)




7. Give two sets of polar coordinates that could be used to plot the given point. (4 points)



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