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Return to Foundations of Science Mathematics 2e Student Resources
Chapter 7 Multiple choice questions
Complex numbers
Quiz Content
*
not completed
.
What are the real and imaginary parts of
z
= (2 + 3
i
) / (3 – 2
i
) ?
Re{
z
} = 1 and Im{
z
} = 0.
correct
incorrect
Re{
z
} = 0 and Im{
z
} = 1.
correct
incorrect
Re{
z
} = 2/3 and Im{
z
} = 3/2.
correct
incorrect
Re{
z
} = 2/3 and Im{
z
} = 3/2.
correct
incorrect
*
not completed
.
What are the modulus and argument of
z
= –1 –
i
√3 ?

z
 = 2 and arg{
z
} = π/3 + 2nπ where n is an integer.
correct
incorrect

z
 = 2 and arg{
z
} = 4π/3 + 2nπ where n is an integer.
correct
incorrect

z
 = 2 and arg{
z
} = π/6 + 2nπ where n is an integer.
correct
incorrect

z
 = 2 and arg{
z
} = 5π/6 + 2nπ where n is an integer.
correct
incorrect
*
not completed
.
Which of the following is
not
true about complex numbers?
Re{
z
_{1}
+
z
_{2}
} = Re{
z
_{1}
} + Re{
z
_{2}
}
correct
incorrect
Re{
z
_{1}
x
z
_{2}
} = Re{
z
_{1}
} x Re{
z
_{2}
}
correct
incorrect

z
_{1}
x
z
_{2}
 = 
z
_{1}
 x 
z
_{2}

correct
incorrect
arg{
z
_{1}
x
z
_{2}
} = arg{
z
_{1}
} + arg{
z
_{2}
}
correct
incorrect
*
not completed
.
Which of the following is
not
true in the context of complex numbers?
An
n
^{th}
order polynomial has
n
roots.
correct
incorrect
The imaginary part of logarithm is multivalued.
correct
incorrect
Positive integer powers of a number are unique.
correct
incorrect
(
z
+ 1)
^{7}
– (
z
– 2)
^{7}
= 0 has 7 roots.
correct
incorrect
*
not completed
.
Which one of the following hyperbolic relationships is correct?
cosh
^{2}
(
x
) – sinh
^{2}
(
x
) = 1
correct
incorrect
1 + tanh
^{2}
(
x
) = sech
^{2}
(
x
)
correct
incorrect
1 + coth
^{2}
(
x
) = cosech
^{2}
(
x
)
correct
incorrect
None of the above.
correct
incorrect
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