Problem 1 :
For i = √-1, which of the following is equivalent to
(5 - 3i) - (-2 + 5i) ?
(a) 3 - 8i (b) 3 + 2i (c) 7 - 8i (d) 7 + 2i
Solution :
= (5 - 3i) - (-2 + 5i)
Distributing the negative, we get
= 5 - 3i + 2 - 5i
= 7 - 8i
So, option c is correct.
Problem 2 :
Given that i = √-1, which of the following is equal to i(i + 1) ?
(a) i - 2 (b) i - 1 (c) i + 1 (d) 0
Solution :
= i(i + 1)
= i2 + i
= -1 + i
So, option b is correct.
Problem 3 :
i4 + 3i2 + 2
Which of the following is equal to the expression above.
(a) i (b) - 1 (c) 0 (d) 1
Solution :
= i4 + 3i2 + 2
= (i2)2 + 3i2 + 2
= (-1)2 + 3(-1) + 2
= 1 - 3 + 2
= 0
Problem 4 :
(6 + 2i) (2 + 5i)
If the expression above is equivalent to a + ib, where a and b are constants. What is the value of a?
(a) 2 (b) 12 (c) 22 (d) 34
Solution :
= (6 + 2i) (2 + 5i)
= 12 + 30i + 4i + 10
= 22 + 34i
a + ib = 22 + 34i
Comparing the corresponding terms, we get
a = 22 and b = 34
So, answer is option d.
Problem 5 :
Which of the following is equal to
3(i + 2) - 2(5 - 4i)?
(a) 16 - 5i (b) -4 + 7i (c) -4 + 11i (d) 16 + 11i
Solution :
= 3(i + 2) - 2(5 - 4i)
= 3i + 6 - 10 + 8i
= 3i + 8i + 6 - 10
= 11i - 4
So, option c is correct.
Problem 6 :
Which of the following equivalent to 3i(i + 2) - i(i - 1) ?
(a) -4 + 7i (b) -2 + 7i (c) -4 + 5i (d) -2 + 5i
Solution :
= 3i(i + 2) - i(i - 1)
= 3i2 + 6i - i2 + i
By combining real and imaginary, we get
= 7i + 2i2
= 7i + 2(-1)
= 7i - 2
= -2 + 7i
So, option b is correct.
Problem 7 :
Which of the following is equivalent to i93 ?
(a) -1 (b) 1 (c) -i (d) i
Solution :
= i93
= i92 (i)
= (i2)46 (i)
= (-1)46 (i)
= 1 (i)
= i
So, the answer is i.
Problem 8 :
Which of the following complex number is equivalent to
(3 - i)2 ?
(a) 8 - 6i (b) 8 + 6i (c) 10 - 6i (d) 10 + 6i
Solution :
= (3 - i)2
Expand this using algebraic identity
(a - b)2 = a2 - 2ab + b2
= 32 - 2(3)i + i2
= 9 - 6i + (-1)
= 9 - 1 - 6i
= 8 - 6i
Problem 9 :
(5 - 2i)(4 - 3i)
Which of the following is equal to the expression above ?
(a) 14 - 7i (b) 14 - 23i (c) 26 + 7i (d) 26 - 23i
Solution :
= (5 - 2i)(4 - 3i)
= 20 - 15i - 8i + 6i2
= 20 - 23i + 6(-1)
= 20 - 23i - 6
= 14 - 23i
So, option b is correct,
Problem 10 :
Which of the following is equal to
(a) -i (b) i (c) 0 (d) 1
Solution :
Option a is correct.
Problem 11 :
Which of the following is equal to
(a) -i (b) i (c) (-5/4)i (d) (3/4) - (5/4)i
Solution :
So, option a is correct.
Problem 12 :
Which of the following complex number is equivalent to
(2 - i)/(2 + i) ?
Solution :
May 21, 24 08:51 PM
May 21, 24 08:51 AM
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