Complex Numbers Questions and Answers

This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Complex Numbers-1”.

1. Value of i(iota) is ____________
a) -1
b) 1
c) (-1)^1/2
d) (-1)^1/4
View Answer

Answer: c
Explanation: Iota is used to denote complex number.
The value of i (iota) is \(\sqrt{-1}\) i.e. (-1)^1/2.

2. Is i(iota) a root of 1+x²=0?
a) True
b) False
View Answer

Answer: a
Explanation: 1+x² = 0
1 + i² = 1 – 1 = 0.
So, it is a root of 1 + x² = 0.

3. In z=4+i, what is the real part?
a) 4
b) i
c) 1
d) 4+i
View Answer

Answer: a
Explanation: In z=a+bi, a is real part and b is imaginary part.
So, in 4+i, real part is 4.

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4. In z=4+i, what is imaginary part?
a) 4
b) i
c) 1
d) 4+i
View Answer

Answer: c
Explanation: In z=a+bi, a is real part and b is imaginary part.
So, in 4+i, imaginary part is 1.

5. (x+3) + i(y-2) = 5+i2, find the values of x and y.
a) x=8 and y=4
b) x=2 and y=4
c) x=2 and y=0
d) x=8 and y=0
View Answer

Answer: b
Explanation: If two complex numbers are equal, then corresponding parts are equal i.e. real parts of both are equal and imaginary parts of both are equal.
x+3 = 5 and y-2 = 2
x = 5-3 and y = 2+2
x=2 and y=4.

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6. If z₁ = 2+3i and z₂ = 5+2i, then find sum of two complex numbers.
a) 4+8i
b) 3-i
c) 7+5i
d) 7-5i
View Answer

Answer: c
Explanation: In addition of two complex numbers, corresponding parts of two complex numbers are added i.e. real parts of both are added and imaginary parts of both are added.
So, sum = (2+5) + (3+2) i = 7+5i.

7. 0+0i is ______________________for complex number z.
a) additive inverse
b) additive identity element
c) multiplicative identity element
d) multiplicative inverse
View Answer

Answer: b
Explanation: On adding zero (0+0i) to a complex number, we get same complex number so 0+0i is additive identity element for complex number z i.e. z+0 = z.

8. 1+0i is _________________ for complex number z.
a) additive inverse
b) additive identity element
c) multiplicative identity element
d) multiplicative inverse
View Answer

Answer: c
Explanation: On multiplying one (1+0i) to a complex number, we get same complex number so 1+0i is multiplicative identity element for complex number z i.e. z*1=z.

9. -z is _________________ for complex number z.
a) additive inverse
b) additive identity element
c) multiplicative identity element
d) multiplicative inverse
View Answer

Answer: a
Explanation: On adding negative of complex number (-z) to complex number z, we get additive identity element zero i.e. z+(-z)=0.

10. 1/z is _________________ for complex number z.
a) additive inverse
b) additive identity element
c) multiplicative identity element
d) multiplicative inverse
View Answer

Answer: d
Explanation: On multiplying reciprocal of complex number (1/z) to complex number z, we get multiplying inverse one i.e. z*1=z.

11. If z₁ = 2+3i and z₂ = 5+2i, then find z₁-z₂.
a) -3+1i
b) 3-i
c) 7+5i
d) 7-5i
View Answer

Answer: a
Explanation: In subtracting one complex number from other, difference of corresponding parts of two complex numbers is calculated. So, z₁-z₂ = (2-5) + (3-2) i = -3+1i.

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