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Algebra II & Trigonometry
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Complex Numbers Review
Part I
In 1 – 14 select the numeral preceding the word or expression that best completes the statement or answers the question.
1. What is the product of 5   36 and 1   49 expressed in simplest a + bi form?
(1) –37 + 41i
(2) 5 – 71i
(3) 47 + 41i
(4) 47 – 29i
2. The expression i 25 is equivalent to
(1) 1
(2) –1
(3) i
(4) –i
3. Which is a true statement about the graph of the equation y  x 2  7x  60 ?
(1) It is tangent to the x-axis.
(2) It does not intersect the x-axis.
(3) It intersects the x-axis in two distinct points that have irrational coordinates.
(4) It intersects the x-axis in two distinct points that have rational coordinates.
4. Which quadratic equation has the roots 3 + i and 3 – i?
(1) x 2  6 x  10  0
(3) x 2  6 x  10  0
(2) x 2  6 x  8  0
(4) x 2  6x  8  0
5. What is the minimum point of the graph of the equation y  2x 2  8x  9 ?
(1) (2, 33)
(2) (2, 17)
(3) (–2, –15)
(4) (–2, 1)
6. For which equation is the sum of the roots equal to the product of the roots?
(1) x 2  x  1  0
(3) x 2  8 x  4  0
(2) x 2  3x  6  0
(4) x 2  4 x  4  0
7. If the equation x 2  kx  36  0 has x = 12 as one root, what is the value of k?
(1) 9
(2) –9
(3) 3
(4) –3
8. What is the multiplicative inverse of 3i ?
(1) –3i
(2) –3
(3)
1
3
(4) 
i
3
9. The roots of the equation 2 x 2  5  0 are
(1) imaginary
(2) real, rational, and equal
(3) real, rational, and unequal
(4) real and irrational
10. For which positive value of m will the equation 4x 2  mx  9  0 have roots that are real, equal, and rational?
(1) 12
(2) 9
(3) 3
(4) 4
11. When expressed as a monomial in terms of i, 2  32  5  8 is equivalent to
(1) 2 2i
(2) 2i 2
(3)  2i 2
(4) 18i 2
12. Which graph represents a quadratic function with a negative discriminant?
13. Two complex numbers are graphed to the right. What is the
sum of w and u, expressed in standard complex number form?
(1) 7 + 3i
(3) 5 + 7i
(2) 3 + 7i
(4) 5 + 3i
Part II
1. The complex number c + di is equal to 2  i 2 . What is the value of c?
2. In physics class, Taras discovers that the behavior of electrical power, x, in a particular circuit can be represented by the
function y  x 2  2x  7 . If y  0 , solve the equation and express your answer in simplest a + bi form.
3. Graph the inequality y  x 2  2x  8 on the grid below.
4. Solve the following system of equations algebraically.
y  x 2  2
x  y 1