Mathematics Questions and Answers – Complex Numbers-1

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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.
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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.
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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.
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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.

Sanfoundry Global Education & Learning Series – Mathematics – Class 11.

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter