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Name: _____________________________________________________________
Pre-Calc Midterm Review – Complex Numbers
1. In simplest form,
300 is equivalent to
A. 5i 12
B. 10i 3
C. 12i 5
D. 3i 10
Date: ____________________
2. What is the conjugate of the complex number 5  4i ?
A. 5  4i
B. 5  4i
C. 5  4i
D. 5  4i
3. What is 4i 3 equivalent to?
A. 4
B. 4i
C. 4i
D. 4
4. In which quadrant does the sum of 2  3i and 1  6i
lie?
A. I
B. II
C. III
D. IV
5. Evaluate and simplify in a  bi : (3  8i)  (4  6i)
A. 7  14i
B. 7  2i
C. 7  2i
D. 1  2i
6. Evaluate and simplify in a  bi : (7  11i)  (7  3i)
A. 0  14i
B. 0  14i
C. 14  14i
D. 0  8i
7. Two complex numbers are graphed below.
8. The relationship between voltage, E , current, I , and
resistance, Z , is given by the equation E  IZ . If a
circuit has a current I  3  2i and a resistance Z  2  i ,
what is the voltage of this circuit?
A. 4  i
B. 8  i
C. 4  i
D. 8  7i
What is the sum of w and u , expressed in standard
complex number form?
A. 5  7i
B. 7  3i
C. 5  3i
D. 3  7i
9. What is the product of 5  2i and i ?
A. 5  2i
B. 7
C. 2  5i
D. 2  5i
10. The expression (1  i)3 is equivalent to
A. 2  2i
B. 2  2i
C. 1  i
D. 3i
11. Simplify in a  bi form:
3
2  3i
12. Find the multiplicative inverse of 4  3i .
Using vectors, demonstrate each expression below geometrically and write an answer.
13.
 6  7i    4  8i 
14.
 6  4i    7 1i 
15. Find the distance between the following points on the complex plane: A  5  7i and B  9  6i
16. Find the midpoint between the following points on the complex plane: A  6 10i and B  2  4i
For each example below, find the modulus and argument. Then, write the number in polar form.
17. w  4  4i
18. z  3  3i
Change the following to rectangular form.


19. 4  cos

4
 i sin


4
20.
1
 cos150  i sin150 
2
For each example below, describe the geometric effect on a complex number w of each operation shown.
22. iw
21. 6w
23. w
25. w y if y  3  3i
24. w  z if z  4  7i
26.
w
if y  3  3i
y
The expression (2  i)2 is equivalent to
A. 5  4i
B. 3
C. 3  4i
D. 5