1. Precalculus
Chapter 9 Study Guide
Define:
Absolute Value of a Complex number
Complex Conjugates
Imaginary Number
Modulus
Polar Axis/Plane
Polar Coordinates
Polar Form of a Complex number
Rectangular Form of a Complex number
Find the rectangular coordinates of the following polar coordinates:
1. (6, 45° ) 2. (2, 330°)
æ 3p ö  π
3. ç −2, ÷
è
4.  1, 
 2
4 ø
Find the polar coordinates of the following rectangular coordinates:
5. ( − 3, - 3) 6. (5, 5)
7. (-3, 1) 8. (4, 2)
Write the equation in polar form. Round φ to the nearest degree.
9. 2x + ψ= −3 10. y = −3ξ − 4
11. 2x − 2 ψ= 6
Write each equation in rectangular form.
 π  π
12. 3 = ρχοσ θ −  13. 4 = ρχοσ θ + 
 3  2
Simplify the complex numbers.
14. i10 + ι25 15. ( 2 + 3ι) − ( 4 − 4 ι)
16. ( 2 + 7ι) + ( −3 − ι) 17. i 3 ( 4 − 3ι)
4 + 2ι
18. (i − 7 ) ( −ι + 7 ) 19.
5 − 2ι
5+ι
20.
1 − 2ι
Convert the complex number into polar form.
21. 2 + 2ι 22. −6 - 4i
23. 4 24. 3i

2. Find each product or quotient. Express the result in rectangular form.
 π π  π π
25. 4  cos + ι σ  ⋅ 3  χοσ + ι σ 
ιν ιν
 3 3  3 3
 π π  π π
26. 8  cos + ι σ  ⋅ 4  χοσ + ι σ 
ιν ιν
 4 4  2 2
 7π 7π   5π 5π 
27. 8  cos + ισιν  ÷ 2  χοσ + ι σιν 
 6 6   3 3
Find the power. Express the result in rectangular form.
8 7
28. ( 2 + 2ι) 29. ( 3 − ι)
( −1 + i ) ( −2 - 2i )
4 3
30. 31.
32. i1/ 4 33. 3
3+ι