Math | Graded Assignment | Practice: Complex Numbers Name: Gaby Granados Garcia Date: Spring 2016 Graded Assignment Practice: Complex Numbers Answer the following questions using what you've learned. Write your responses in the space provided, and turn the assignment in to your instructor. For questions 1-3 the polar coordinates of a point are given. Find the rectangular coordinates of each point. 1. ( 5 sqrt 2/ 2 , 5 sqrt 2/2) 2. (-sqrt3 , -1) 3. (1/2 , - sqrt3/2) For questions 4-6 the rectangular coordinates of a point are given. Find the polar coordinates of each point. 4. (4,0 degrees) 5. (3,90 degrees) 6. (2 sqrt 2 , 45 degrees) 7. Give two sets of polar coordinates that could be used to plot the given point. (4, 5pi/6) (4, 150 degrees) (a) 2015 K12 Inc. All rights reserved. Copying or distributing without K12's written consent is prohibited. Page 1 of 4 Math | Graded Assignment | Practice: Complex Numbers (4, 3pi/2) (4, -pi/2) (b) 8. Graph each polar equation. Write the scale you are using for the polar axis. (a) (b) 9. Transform each polar equation to an equation in rectangular coordinates and identify its shape. (a) (sqrt(3)/2, 1/2) 2015 K12 Inc. All rights reserved. Copying or distributing without K12's written consent is prohibited. Page 2 of 4 Math | Graded Assignment | Practice: Complex Numbers (b) 10. Compute the modulus and argument of each complex number. (a) (b) 5 - 5i 11. Write each complex number in rectangular form. Plot and label each point on the polar axes below. (a) (b) (c) (d) (e) (f) 12. Let . (a) Convert z and w to polar form. (b) Calculate zw. (c) Calculate z=(5, 5pi/6) w=(2, pi/3) zw= -5 sqrt3 - 5i . z/w = 5/2 i For questions 7-12, let . Calculate the following, keeping your answer in polar form. 13. 14. 15. 16. 17. 18. ; Use your answer to #15: 2015 K12 Inc. All rights reserved. Copying or distributing without K12's written consent is prohibited. Page 3 of 4 Math | Graded Assignment | Practice: Complex Numbers For questions 19-22, write each expression in the standard form for a complex number, a + bi. 19. ; Use De Moivre's Theorem -32 sqrt2 + 32i sqrt2 20. ; Use De Moivre's Theorem 0.598 + 0.57543960i 21. The complex fourth roots of . 5 sqrt2(cos(-pi/4)+i sin(- pi/4)) 22. The complex cube roots of . 6.47 + 4.70228201i 23. Find all seventh roots of unity and sketch them on the axes below. 2015 K12 Inc. All rights reserved. Copying or distributing without K12's written consent is prohibited. Page 4 of 4