Complex Number Problems Worksheet
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1Complex Number Exercises
CS 145 Images and Imagination
1. Put in z standard form (a + b i):
a. z = 4 + 16 = _______________
i +
2
b. z =
i
25
= _______________
2
c. z = -72
i + i = _______________
5
d. z =
i = _______________
2. Convert from polar to standard form (Cartesian coordinates) in standard form
a. r = 4, θ = 25, z = ________
b. r = 5, θ = 200 z = ________
3. Compute the modulus (length) of
a. z = 2 + 4 i,
r = ________
b. z = -3 + 1.5 i, r = ________
4. What is the z = complex conjugate of each of the z values in problem 3
a. z = _________
b. z = _________
5. Suppose z
= (1 + 3 i) and z
= (-2 + 4 i). Calculate the following, placing the result
1
2
in standard form
a.
z +
z = _____________
1
2
b.
z -
z = _____________
1
2
c. 2
z = _____________
1
2
d.
z
z =
z
= _____________
1
1
1
e.
z
z
= _____________
1
2
z +
f.
z
= ______________
1
1
g.
z
z
= ______________
1
1
h.
z /
z = _____________
1
2
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