Download Institution: University of the West Indies (St. Augustine) Lecturer: Mr

Institution: University of the West Indies (St. Augustine)
Course: Engineering Mathematics I (MATH 1180), Group I: Class Quiz #1
Lecturer: Mr. Oral Robertson
Date: September 23, 2010
MATH 1180: Class Quiz #1  COMPLEX NUMBERS (Multiple Choice)
Duration of Test: 50 mins.
Instructions: This paper has twenty (20) questions. Circle the correct answer (a), (b), (c), or (d).
 The use of calculators is NOT ALLOWED.
NAME: _____________________________________________
I.D.# : __________________________
1. What is the value of i5 ?
(a)
i
(b) –1
(c)
–i
(d) 1
2. If z = –3 – 4i, what is the value of Im(z) ?
(a) –3
(b) –3i
(c) –4
(d) –4i
3. Which of the following gives the correct centre and radius of the circle defined by: |z – 2 + 3i|= 4 ?
(a) (–2, 3) and 4 units
(b) (–2, 3) and 2 units
(c) (2, –3) and 4 units
(d) (2, –3) and 2 units
4. If z1 = a + bi and z 2 = c + di, then the product z 1 z 2 equals to?
(a) (ac + bd) + i(–ad + bc)
(b) (ac – bd) + i(ad + bc)
(c) (ac + bd) + i(ad – bc)
(d) (ac – bd) + i(–ad – bc)
5. Taking what you know of complex number conjugates (including their geometry), which of the
following do you expect to be not true?
(a) z 2  z z
(b) Re(z)  Re( z)
6. What is the value of arg(–1)?
(a) 0
(b) /2
(c) z  z  2 Im(z) i
(d) z1  z 2  z1  z 2
(c) 
(d) 3/2
7. What expression gives the length of the line segment connecting two complex numbers z2 and z3 ?
(a) |z3 – z2|
(b) |z2 + z3|
(c) |z3| – |z2|
(d) |z2| + |z3|
8. When the complex number “ i tanh ix ” is simplified, you get ?
(a) – tanh x
(b) tanh x
(c) – tan x
(d) tan x
9. If z = cos + i sin, then which of the following is not true?
(a) z = ei
(b) |z| = 1
(c) 1/z = cos – i sin
(d) arg(z) = tan
10. What expression below gives the complex number  1  i 3 in polar form?
(a) 2 cos 2  i sin 2 

3
3 
(b) 4 cos   i sin  

3
3
(c) 2 cos 4  i sin 4 

3
3 
(d) 4 cos 5  i sin 5 

3
3 
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Institution: University of the West Indies (St. Augustine)
Course: Engineering Mathematics I (MATH 1180), Group I: Class Quiz #1
Lecturer: Mr. Oral Robertson
Date: September 23, 2010
11. What statement describes the point P (representing a complex number z) such that its distance from
the point (0, –1) is twice its distance from the point (3, 0) ?
(a) z  1  2 z  3i
(b) z  1  2 z  3i
(c) z  i  2 z  3
(d) z  i  2 z  3
12. Which of the following is not true for two general complex numbers z1 and z 2 ?
(a) z1 z 2  z1 z 2
(b) z1  z 2  z 1  z 2
13. If z = cos + i sin, then z  1
(a) 2 cos
z
(b) 2 sin
(c) z1 z 2  z1 z 2
(d) z1 z 2  z1 z 2
= ?
(c) 2i cos
14. What is the value of Im(w) given that w = cos(x – iy) ?
(a) cos x cosh y
(b) sin x cosh y
(c) cos x sinh y
(d) 2i sin
(d) sin x sinh y
 z  n 
15. If two complex numbers are z1 = r1(cos1 + i sin1) and z2 = r2(cos2 + i sin2), then arg 2   equals ?
 z1  
nθ 2
n
n
n
(a)
(b) θ 2  θ 1 
(c) nθ 2  θ1 
(d) θ 2  θ1
θ1
16. If z = cos + i sin, then z n  1
(a) 2 cos n
zn
(b) 2n cos 
= ?
(c) 2i sin n
(d) –2n sin n
17. Which of the following is not true for two complex numbers z1 and z 2 ?
(a) z1  z 2  z1  z 2
(b) z1  z 2  z1  z 2
(c) z1 z 2  z1 z 2
(d) z1  z 2  z 2  z1
18. Graphically, which of the following is not true for a complex number z1 defined by arg z1 =
(a) y > 0
(b) x < 0
(c) y = –x
3
?
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(d) y = x
19. On an Argand diagram, two complex numbers z1 and z2 are such that arg(z2) > arg(z1). What expression
can accurately give the angle between the two lines Oz1 and Oz2 ?
(a) arg(z1 + z2)
(b) arg (z2 – z1)
(c) arg(z2/z1)
(d) arg(z1 z2)
20. If w = cos2 + i sin2, then which of the following is NOT an expression equivalent to Re(w)?
(a) cos2 + sin2
(b) cos2 – sin2
(c) 2cos2 – 1
(d) 1 – 2sin2
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