42
Math 1083 Worksheet 17 Getting Ready for Polar Form of Complex Numbers
Objectives:
1. Complex numbers
2. Polar coordinates
3. Evaluate trigonometric expressions
(1)Complex numbers
A complex number is a number = + where x and y are real numbers, x is the real part of
the complex number and y is the imaginary part of the complex number i =√− .
#1 Simplify and write the number in form of + .
a) 5 + √−4 b) 3 − √−9
c) 2− √−9 + √−16 + √25 d) −7 + √−25 + √49 + √−36
Plotting = + on the graph is the same way plotting point ( , ) on the rectangular
coordinates.
#2 Plot the given complex numbers on the complex plane on the left.
1 = −2 + 3 → ( , ) =________________
2 = 4 − 5 → ( , ) =________________
3 = 3 − + 5 + 4 =______________→
( , ) =________________
3 = −6 − √−9 + √−25 + √64 =______________
→ ( , ) =________________
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REVIEW:
2 +
2 =
2
cos θ =
, sin =
#3 Find the quadrant of the given point. Then convert to polar form (r, ) where 0 ≤ <
a) A(3, −3) b) B(2, 2 √3)
c) B( −√3, −1) d) D(0, −5)
#4 Find and using the given values.
a) = 2, =
2
3
b) = 4, =
−
4
=____________ =____________ =____________ =____________
#5 Let 1 = 3, 2 = 4, 1 =
12
2 =
11
12
Evaluate each expression.
a) 1 2 ( 1 + 2) b) 1
4
sin(3 1) c) 2
1
cos ( 2 − 1)
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