Complex Numbers - Mathematics Multiple Choice Questions 2

This set of Mathematics Question Bank focuses on “Complex Numbers-2”.

1. z₁=1+2i and z₂=2+3i. Find z₁z₂.
a) 2+6i
b) -4+0i
c) -4+7i
d) 8+7i
View Answer

Answer: c
Explanation: z₁z₂ = (1+2i) (2+3i)
= 2 + 3i + 4i -6
= -4 + 7i.

2. i² =______________________
a) 1
b) -1
c) i
d) -i
View Answer

Answer: b
Explanation: We know, i = \(\sqrt{-1}\)
=> i² = -1.

3. i⁷ =______________
a) 1
b) -1
c) i
d) -i
View Answer

Answer: d
Explanation: We know, i = \(\sqrt{-1}\)
=> i² = -1 => i⁴ = 1.
So, i⁷ = i⁴.i³ = 1*i²*i = (-1)*i = -i.

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4. i²⁴¹ =________________
a) 1
b) -1
c) i
d) -i
View Answer

Answer: c
Explanation: We know, i = \(\sqrt{-1}\)
=> i² = -1 => i⁴ = 1.
So, i²⁴¹ = (i⁴)⁶⁰ * i = 1 * i = i.

5. Square roots of -7 are____________
a) 7i and -7i
b) \(\sqrt{7}\) i
c) –\(\sqrt{7}\) i
d) \(\sqrt{7}\) i and –\(\sqrt{7}\) i
View Answer

Answer: d
Explanation: We know, i² = -1.
-7 = 7(i²)
Square root of i² is ±i so, square root of -7 are \(\sqrt{7}\)i and –\(\sqrt{7}\)i.

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6. (-i) (8+5i) =________________
a) 8+5i
b) -8-5i
c) -5-8i
d) 5-8i
View Answer

Answer: d
Explanation: (-i) (8+5i) = -8i – 5 i²
= -8i -5(-1) = 5-8i.

7. (2-i)³ =________________
a) 2-3i
b) 8-i
c) 2-11i
d) 2+11i
View Answer

Answer: c
Explanation: We know, (a-b)³ = a³-b³-3ab(a-b)
So, (2-i)³ = 2³-(i)³-3(2)(i) (2-i)
= 8-(-i)-6i(2-i)
= 8+i-12i-6
= 2-11i.

8. Is z*\(\bar{z}\) = |z|²?
a) True
b) False
View Answer

Answer: a
Explanation: Let z=a+ bi
=>\(\bar{z}\) = a-bi
So, z*\(\bar{z}\) = (a+bi) (a-bi) = a²-(bi)² = a²-(b²) (-1) = a²+b²
|z|=\(\sqrt{a^2+b^2}\) => |z|² = a²+b²
Hence, z*\(\bar{z}\) = |z|².

9. Find multiplicative inverse of 3+5i.
a) 87+145i
b) 87-145i
c) 145-87i
d) 145+87i
View Answer

Answer: b
Explanation: We know, z*\(\bar{z}\) = |z|².
(1/z) = \(\bar{z}\)|z|²
z^-1=(3-5i) (3²+5²) = (3-5i) (29) = 87-145i.

10. i^-35 =___________________
a) 1
b) -1
c) i
d) -i
View Answer

Answer: c
Explanation: We know, i^-35= 1/i³⁵ = i/i³⁶
= i/(i⁴)⁹ = i/1 = i.

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