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

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+x^{2}=0?

a) True

b) False

View Answer

Explanation: 1+x

^{2}= 0

1 + i

^{2}= 1 – 1 = 0.

So, it is a root of 1 + x

^{2}= 0.

3. In z=4+i, what is the real part?

a) 4

b) i

c) 1

d) 4+i

View Answer

Explanation: In z=a+bi, a is real part and b is imaginary part.

So, in 4+i, real part is 4.

4. In z=4+i, what is imaginary part?

a) 4

b) i

c) 1

d) 4+i

View Answer

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

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.

6. If z_{1} = 2+3i and z_{2} = 5+2i, then find sum of two complex numbers.

a) 4+8i

b) 3-i

c) 7+5i

d) 7-5i

View Answer

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

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

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

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

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 z_{1} = 2+3i and z_{2} = 5+2i, then find z_{1}-z_{2}.

a) -3+1i

b) 3-i

c) 7+5i

d) 7-5i

View Answer

Explanation: In subtracting one complex number from other, difference of corresponding parts of two complex numbers is calculated. So, z

_{1}-z

_{2}= (2-5) + (3-2) i = -3+1i.

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