Download Complex Numbers Worksheet

Name
Gifted Advanced Algebra
_____
COMPLEX NUMBERS AND SOLVING QUADRATICS TEST REVIEW
1. For the complex number 10  4i , identify the real number and the imaginary number.
𝑖3
2. Evaluate.
a) i 6
b) i11 𝑖 3
c) (𝑖 2 )10
d) 6
𝑖
3. Subtract (8-3i) from its conjugate.
4. Write the expression as a complex number in standard form.
a)  5  2i    3  2i 
b) i   7  5i   3  2  3i 
c)  2  4i    3  9i 
d)  2  4i    3  9i 
e)  5  2i   2 3  i 
f) 3i  6  5i 
g) i  2  i 
h)  2  3i 1  4i 
i)  3  7i 1  2i 
j)  3  2i 
k)  2i 1  4i 1  i 
2
5. Write the expression as a complex number in standard form.
2  4i
8  7i
5
a)
b)
c)
7i
3  4i
1 i
d)
4  4i
2  9i
6. Solve each equation. Use each method at least once. (sq rt, QF, comp the square)
a) 4 x2  20  0
b) 4 x2  5  7
c) x2  4x  20
d) x2  8x  35
e) x2  4x  29
f) 3  x  4   27
2
g) 8r 2  4r  5  0
h) 6 p 2  8 p  3
Name
Gifted Advanced Algebra
_____
COMPLEX NUMBERS AND SOLVING QUADRATICS TEST REVIEW
1. For the complex number 10  4i , identify the real number and the imaginary number.
a) i 6
2. Evaluate.
b) i11 𝑖 3
c) (𝑖 2 )10
3. Subtract (8-3i) from its conjugate.
4. Write the expression as a complex number in standard form.
a)  5  2i    3  2i 
b) i   7  5i   3  2  3i 
d)
𝑖3
𝑖6
c)  2  4i    3  9i 
d)  2  4i    3  9i 
e)  5  2i   2 3  i 
f) 3i  6  5i 
g) i  2  i 
h)  2  3i 1  4i 
i)  3  7i 1  2i 
j)  3  2i 
k)  2i 1  4i 1  i 
2
5. Write the expression as a complex number in standard form.
2  4i
8  7i
5
a)
b)
c)
7i
3  4i
1 i
d)
4  4i
2  9i
6. Solve each equation. Use each method at least once. (sq rt, QF, comp the square)
a) 4 x2  20  0
b) 4 x2  5  7
c) x2  4x  20
d) x2  8x  35
e) x2  4x  29
f) 3  x  4   27
2
g) 8r 2  4r  5  0
h) 6 p 2  8 p  3
Answers
1.
2.
3.
4.
Real number: 10 ; Imaginary number: 4i
a) -1
b) -1
c) 1
6i
a) 8
b) 1  3i
c) 1  5i
h) 14  5i
i) 11  13i
j) 5-12i
5  5i
2
6. a) i 5
5. a)
g)
−1±3𝑖
4
b)
4−2𝑖
−7
𝑜𝑟
b) i 3
−4+2𝑖
c)
7
d) i
d) 5  5i
e) 1  4i
f) 15 18i
g) 1  2i
2
2
k)  2i  1  3i  4i   2i  5  3i   10i  6i  6  10i

−4+53𝑖
25
h)
4±𝑖 √2
6
or


28+44𝑖
85
d) 4  i 19
c) 2  4i
1 3i
or  
4 4
d)

e) 2  5i
f) 4  3i
2 i 2

3
6
Answers
1.
2.
3.
4.
Real number: 10 ; Imaginary number: 4i
a) -1
b) -1
c) 1
6i
a) 8
b) 1  3i
c) 1  5i
h) 14  5i
i) 11  13i
j) 5-12i
5  5i
2
6. a) i 5
5. a)
g)
−1±3𝑖
4
b)
4−2𝑖
−7
b) i 3
1 3i
or  
4 4
𝑜𝑟
−4+2𝑖
c)
7
d) i
d) 5  5i
e) 1  4i
f) 15 18i
g) 1  2i
2
2
k)  2i  1  3i  4i   2i  5  3i   10i  6i  6  10i

−4+53𝑖
25
4±𝑖 √2
6
or
2 i 2

3
6

28+44𝑖
d) 4  i 19
c) 2  4i
h)
d)

85
e) 2  5i
f) 4  3i
