System of Numbers and Conversion Reviewer Part 3

Continue Practice Exam Test  A. 5
B. 1
Questions Part 3 of the Series 
 C. 2
Choose the letter of the best answer  D. 3
in each questions.

Problem 101 (CE May 1994) Problem 106

In the complex number 3 + 4i, the Multiply (3-2i)(4+3i).
absolute value is:
 A. 12 + i
 A. 10  B. 18 + i
 B. 7.211  C. 6 + i
 C. 5  D. 20 + i
 D. 5.689

Problem 107 (EE October 1997)
Problem 102
Divide ((4 + 3i)/(2 – i)).
In the complex number 8-21, the
amplitude is:  A. ((11 + 10i)/5)
 B. 1 + 2i
 A. 104.04°  C. ((5 + 2i)/5)
 B. 14.04°  D. 2 + 2i
 C. 345.96°
 D. 165.96°
Problem 108

Problem 103 Find the value of i9.

(6 cis 120°)(4 cis 30°) is equal to:  A. i
 B. –i
 A. 10 cis 150°  C. 1
 B. 24 cis 150°  D. -1
 C. 10 cis 90°
 D. 24 cis 90°
Problem 109 (ECE April 1999)

Problem 104 Simplify i1997+ i1999, where I is an
imaginary number.
((20 cis 80°)/(10 cis 50°)) is equal to:
 A. 1 + i
 A. 20 cis 30°  B. I
 B. 3 cis 130°  C. 1 – i
 C. 3 cis 30°  D. 0
 D. 20 cis130°

Problem 110
Problem 105
Expand (2 + √-9)3
The value of x + y in the complex
equation 3 + xi = y + 2i is:  A. 46 + 9i
 B. 46 – 9i

,  C. –46 – 9i  D. –8 – 4i
 D. –46 + 9i

Problem 116
Problem 111
What is the exponential form of the
Write –4 + 3i in polar form. complex number 4 + 3i?

 A. 5Լ36.87°  A. 5ei53.13°
 B. 5Լ216.87°  B. 5ei36.87°
 C. 5Լ323.13°  C. 7ei53.13°
 D. 5Լ143.13°  D. 7ei36.87°


Problem 112 Problem 117

Simplify: i30 – 2i25 + 3i17. What is the algebraic form of the complex
number 13ei67.38°?
 A. I + 1
 B. –1 – 2i  A. 12 + 5i
 C. –1 + i  B. 5 – 12i
 D. –1 + 5i  C. 12 – 5i
 D. 5 + 12i

Problem 113 (ME April 1997)
Problem 118 (ME April 1998)
Evaluate the value of √(-10) ● √(-7).
Solve for x that satisfy the equation x2 +
 A. Imaginary 36 = 9 – 2×2.
 B. -√70
 C. √17  A. ±6i
 D. √70  B. ±3i
 C. 9i
 D. -9i
Problem 114 (EE April 1994)

Perform the indicated operation: √(-9) ● Problem 119
3√(-343).
Evaluate ln (5 + 12i).
 A. 21
 B. 21i  A. 2.565 + 1.176i
 C. -21i  B. 2.365 – 0.256i
 D. -21  C. 5.625 + 2.112i
 D. 3.214 – 1.254i

Problem 115 (ECE April 1999)
Problem 120 (EE April 1994)
What is the quotient when 4 + 8i is
divided by i3? Add the given vectors: (-4, 7) + (5, -9)

 A. 8 + 4i  A. (1, 16)
 B. –8 + 4i  B. (1, -2)
 C. 8 – 4i  C. (9, 2)