For questions 1 - 3, the polar coordinates of a point are given. Find the rectangular coordinates of each point. (2 points each) 1. [237"] For questions 4 - 6, the rectangular coordinates of a point are given. Find the polar coordinates of each point. (2 paints each) 4. (4, U) 5. (3, 4) 6. (2, -2) 7. Give two sets of polar coordinates that could be used to plot the given point. (4 points) a. 2x 074 2 3 b.B. 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(58) 27 CO AIN 571 6 0,2x 1 127 6 571 3 3 2 b. r = 2cose CO 0,2x 177 6 6 571 5779. Transform each polar equation to an equation in rectangular coordinates and identify its shape. (4 points) a. 9 = 1.34 radians b. r = tane seco10. Compute the modulus and argument of each complex number. (4 points) a. -5/ b. /10 cos 5x + / sin 5x 7 711. Write each complex number in rectangular form. Plot and label (with a - d) each point on the polar axes below. (4 points) a. 2 [ cos(135)+ /sin(135)) b. 3 cos(120")+ isin(1209)) c. 5 cos 5 + isin 5x d. 4 cos ( 5x )+ isin( 5x ) 0,2 7 6 A w/g12. Let z= 13 + 7/ and w = 3(cos(1.43) + isin(1.43)). (6 points) a. Convert z to polar form. b. Calculate zwusing De Moivre's theorem. c. Calculate _ using De Moivre's theorem. WFor questions 13 - 15, let z, = 2 cos + i sin and zz = 8 cos 7 x 7x 07/ 4 6 + i sin 6 Calculate the following, keeping your answer in polar form. (2 points each) 13. ZIZZ 14. Zz 4For questions 16 - 19, write each expression in the standard form for the complex number a + bi. ( 2 points each) 16. 4 COS + isin 7 x 9 9 5 17. NI- cos(72" ) + / sin (72"))18. The complex fifth roots of 5-5 3i . 19. Find all seventh roots of unity and sketch them on the axes below. 371 4 6 -0,2AT 1 1/T 6 6 4 N