Question 1 :
3i(i + 2) - i(i - 1)
For i = √-1, which of the following is equivalent to the expression above?
A) -4 + 7i
B) -2 + 7i
C) -4 + 5i
D) -2 + 5i
Answer :
= 3i(i + 2) - i(i - 1)
= 3i2 + 6i - i2 + i
Since, i = √-1, we have i2 = -1.
= 3(-1) + 6i - (-1) + i
= -3 + 6i + 1 + i
= -2 + 7i
The correct answer choice is (B).
Question 2 :
Which of the following is equal to (5 + 3i)(5 - 3i)?
(Note : i = √-1)
A) 21
B) 29
C) 21 - 20i
D) 29 + 20i
Answer :
= (5 + 3i)(5 - 3i)
= 52 - 15i + 15i - (3i)2
= 25 - 32i2
= 25 - 9i2
Since, i = √-1, we have i2 = -1.
= 25 - 9(-1)
= 25 + 9
= 34
Question 3 :
For i = √-1, which of the following is equal to i117?
A) -1
B) 1
C) -i
D) i
Answer :
= i117
= i116 + 1
= i116i
= (i2)58i
= (-1)58i
= (1)i
= i
The correct answer choice is (D).
Question 4 :
2 + 3i + 4i2 + 5i3 + 6i4
If the above expression is equivalent to (a + bi), where a and b are constants, what is the value of (a + b)?
(Note : i = √-1)
A) 2
B) 6
C) 10
D) 12
Answer :
a + bi = 2 + 3i + 4i2 + 5i3 + 6i4
a + bi = 2 + 3i + 4i2 + 5i2i + 6(i2)2
Since, i = √-1, we have i2 = -1.
a + bi = 2 + 3i + 4(-1) + 5(-1)i + 6(-1)2
a + bi = 2 + 3i - 4 - 5i + 6(1)
a + bi = 2 + 3i - 4 - 5i + 6
a + bi = 4 - 2i
a = 4 and b = -2
a + b :
= 4 + (-2)
= 4 - 2
= 2
Question 5 :
If the above expression is equivalent to (a + bi), where a and b are constants, what is the value of b?
A) -4/13
B) 4/13
C) -7/13
D) 7/13
Answer :
In the given expression, the denominator is 3i - 2.
To write the given expression in the form (a + ib), multiply both numerator and denominator of the expression by the conjugate of (3i - 2), that is (3i + 2).
The above expression is in the form of (a + ib).
a + ib = (4/13) + (-7/13)i
The value of b is -7/13.
The correct answer choice is (C).
Question 6 :
Which of the following is equal to the expression above?
(Note : i = √-1)
A) -2 - i
B) 2 + i
C) 4 + i
D) 4 - i
Answer :
In the expression above, the common denominator is
(1 + i)(1 - i)
Multiply the numerator and denominator of the first fraction by (1 + i) and the second one by (1 - i) and simplify.
The correct answer choice is (B).
Question 7 :
A) -i
B) i
C) 0
D) 1
Answer :
The correct answer choice is (A).
Question 8 :
If 2xyi + y = 2(1 + i)2 + 5(1 - i), what is the value of x and y?
Answer :
2xyi + y = 2(1 + i)2 + 5(1 - i)
2xyi + y = 2(1 + i)(1 + i) + 5(1 - i)
2xyi + y = 2(1 + i + i + i2) + 5(1 - i)
2xyi + y = 2(1 + 2i - 1) + 5(1 - i)
2xyi + y = 2(2i) + 5(1 - i)
2xyi + y = 4i + 5 - 5i
2xyi + y = 5 - i
2xy = 5 Substitute y = -1. 2x(-1) = 5 -2x = 5 x = -5/2 |
y = -1 |
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