PRECALC 101 6.6.3 Practice: Complex Numbers Practice Precalculus Sem 2

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6.6.3 Practice: Complex Numbers Practice Precalculus Sem 2 Points Possible:50 Name: Sierra Steadman Date: 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. For questions 4 - 6, the rectangular coordinates of a point are given. Find the polar coordinates of each point. (2 points each) 7. a.Give two sets of polar coordinates that could be used to plot the given point. (4 points) a. (2.5, 8pi/3) and (-2.5, 2pi/3)b. (4, 7pi/2) and (-4, pi/2)8. Identify, graph, and state the symmetries for each polar equation. Write the scale that you are using for the polar axis. (4 points) a. r = 9cos(5 ) symmetric about the x-axis b. r = 2cos9. Transform each polar equation to an equation in rectangular coordinates and identify its shape. (4 points) a. = 1.34 radians theta=tan-1(y/x)=1.35radiansTherefore y/x=tan(1.34radians) y/x is about 4.26 y=4.26x The straight line which passes through the origin b. r = tan sec r=tan(theta)sec(theta) + r=sin(theta)/cos(theta)x1/cos(theta) sin(theta)/cos(theta)=tan(theta)=y/x + r=y/x x 1/cos(theta) rcos(theta)=y/x + y=x^2 parabola 10. Compute the modulus and argument of each complex number. (4 points) a. -5i Modulus: |z|=sqrt 0^2 + (-5)^2 = sqrt 25 = 5 Argument: theta=tan-1(-5/0)=tan-1(tan(90))=90 degreesb. Modulus: r=sqrt 10 Argument: theta=5pi/7 11. Write each complex number in rectangular form. Plot and label (with a - d) each point on the polar axes below. (4 points) a. i b. ½-sqrt 3/2 i12. Let z = 13 + 7i and w = 3(cos(1.43) + isin(1.43)). (6 points) a. Convert z to polar form. 14[cos(28)+isin(28)] b. Calculate zw using De Moivre's theorem. 44.295[cos(1.924)+isin(1.924)]c. Calculate using De Moivre's theorem. 4.931[cos(-0.936)+isin(-0.936)] For questions 13 - 15, let and . Calculate the following, keeping your answer in polar form. (2 points each) 13. s 7pi/6-i sin 7 pi/6) 15. z1/z2= ¼(cos(29/30)pi-isin(29/30)pi)For questions 16 - 19, write each expression in the standard form for the complex number a + bi. ( 2 points each) 16. 32+i(32sqrt 3) 18. The complex fifth roots of . 10^(⅕)[cos(11pi/30+8pi/5)+isin(11pi/30+8pi/5)]19. Find all seventh roots of unity and sketch them on the axes below.

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