Math 095 - Intermediate Algebra - Prairie State College

Objective 16: Simplify complex numbers and write in standard form a + bi. [Students
must be prepared to add, subtract, multiply, and divide complex numbers, as well as
write square roots of negative numbers in complex form.]
41. Expand and simplify. Write your result in standard form.
(a) 7i 2 + 2i − 2
(b) 12i 2 + 2i − 2
(c) −14 + 2i
(d) −7 + 2i
(2 + 4i)(3i − 1)
42. Expand and simplify. Write your result as a complex number in standard form.
√
−9(
√
−9 + 1)
(a) −9 + 3i
(b) 9 + 3i
(c) 9 + √ −9
(d) 10
43. Simplify and write in standard form:
(a) −3/2
(b) i
(c) 5i
(d) 2i2 + 5i + 2
−i 2 + 4
1 + 2i
2 − i
Objective 17: Solve all types of quadratic equations, including those with complex solutions.
Solve rational equations that reduce to quadratic equations.
x 2
44. Solve for x:
3 = −2 3 x − 5 3
(a) x = 1 + i or x = 1 − i
(b) x = −1 + 2i or x = −1 − 2i
(c) x = −2 + i or x = −2 − i
(d) x = 4 + 2i or x = 4 − 2i
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