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NAME:__________________________________________________ DATE:________________ REVIEW: COORDINATE SYSTEMS 2-D, 3-D, Complex, Polar POLAR Plot each point with the given polar coordinates. 1. (3, 45) Rename #1 and #2 three different ways. 3. (3, 45) 2 2. 3, 3 2 4. 3, 3 ________ or ________ or ________ ________ or ________ or ________ Find the rectangular coordinates of #5 and #6. USE EXACT VALUE IF POSSIBLE! 5. (3, 45) = __________ 2 6. 3, 3 = __________ Find the polar coordinates for each point with the given rectangular coordinates. USE EXACT VALUE IF POSSIBLE! 7. 3, 3 8. (2, -2) Graph by hand (no y = button!), showing every 15 or 9. r 5sin(2 ) . 12 r r 3D THREE DIMENSIONAL z 10. Write the equation of a sphere with center at 3,5, 2 and radius of 7. 11. Plot the following points, find the midpoint and distance between them. A(3,5,4) B(4,6,3) 12. Find the intercepts of the following: 2 x 3 y 7 z 48 COMPLEX 13. Solve and graph the solutions in the complex plane. Convert each complex number to polar form. 10. 1 – i 11. 2 3 2i Convert each complex number in rectangular form. 12. 3(cos 45 i sin 45) 2 13. 3cis 3 Find all possible roots of x 3 8 . Express solutions in rectangular form. y x Exponential Form re i r (cos i sin ) For 1-9 use the point z1 2e 2 i 3 De Moivre’s Theorem rcis n r n cos n i sin n and z 2 4cis 60 1. Convert z1 to complex polar (trigonometric form). Then graph it! 2. Convert z1 to complex rectangular. Then graph it on the complex plane! 3. Find the absolute value of z1 . 4. Find z1 z 2 . Express your answer in rectangular form. 5. Find z1 . Express your answer in rectangular form. z2 6. Find z1 z 2 . Express your answer in rectangular form. 7. Find z1 . Express your answer in rectangular form. 6 8. Find z1 5 . Express your answers in trigonometric form. 1 9. Find the 5th root of z1 . Express your answer in trigonometric form. SOLVE. Graph your solutions on the complex plane. 10. x 9 11. x 2 2 x 3 0 12. x 8 256 13. x 3 5i MATCHING 14. 15.