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JEE Exam  >  JEE Test  >  Mathematics (Maths) Main & Advanced  >  Test: Introduction To Complex Numbers - JEE MCQ

Introduction To Complex Numbers - Free MCQ Practice Test with solutions,


MCQ Practice Test & Solutions: Test: Introduction To Complex Numbers (15 Questions)

You can prepare effectively for JEE Mathematics (Maths) for JEE Main & Advanced with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Test: Introduction To Complex Numbers". These 15 questions have been designed by the experts with the latest curriculum of JEE 2026, to help you master the concept.

Test Highlights:

  • - Format: Multiple Choice Questions (MCQ)
  • - Duration: 15 minutes
  • - Number of Questions: 15

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Test: Introduction To Complex Numbers - Question 1
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Find the result in the form a + ib of (2-√-25) / (1+√-16)

Detailed Solution: Question 1

Test: Introduction To Complex Numbers - Question 2
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Express the following in standard form :

Detailed Solution: Question 2

first write above equation in complex number format , ie using iota
(3-4i) / (2-3i)*(2+3i) / (2+3i) = (6+9i-8i+12) / 13=(18/13)+(i/13)

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Test: Introduction To Complex Numbers - Question 3
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Find the real numbers x and y such that : (x + iy)(3 + 2i) = 1 + i

Detailed Solution: Question 3

(x + iy)(3 + 2i) = (1 + i)
x + iy = (1 + i)/(3 + 2i)
x + iy = [(1 + i) * (3 - 2i)] / [(3 + 2i)*(3 - 2i)]
x + iy = (3 + 3i - 2i + 2) / [(3)2 + (2)2]
x + iy = (5 + i)/[ 9 + 4]
= (5 + i) / 13
=> 13x + 13iy = 5+i
13x = 5         13y = 1
x = 5/13         y = 1/13

Test: Introduction To Complex Numbers - Question 4
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Find the reciprocal (or multiplicative inverse) of -2 + 5i 

Detailed Solution: Question 4

-2 + 5i
multiplicative inverse of -2 + 5i is
1/(-2+5i)
= 1/(-2+5i) * ((-2-5i)/(-2-5i))
= -2-5i/(-2)^2 -(5i)^2
= -2-5i/4-(-25)
= -2-5i/4+25
= -2-5i/29
= -2/29 -5i/29

Test: Introduction To Complex Numbers - Question 5
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Find the real numbers x and y such that : (x + iy)(3+2i) = 1 + i

Detailed Solution: Question 5

(x + iy) (3 + 2i)
= 3x + 2xi + 3iy + 3i*y = 1+i
= 3x-2y + i(2x+3y) = 1+i
= 3x-2y-1 = 0 ; 2x + 3y -1 = 0  
on equating real and imaginary parts on both sides
on solving two equations
x= 5/13 ; y = 1/13  

Test: Introduction To Complex Numbers - Question 6
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Write in the simplest form: (i)-997

Detailed Solution: Question 6

(i-997) = 1/(i997), 1/((i4)249) × i

Since (i4) = 1, (i4) / i = (i3)

= - i  (Since i2 = -1 , therefore, i3 = - i)

Test: Introduction To Complex Numbers - Question 7
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Express the following in standard form : (8 - 4i) - (-2 - 3i) + (-10 + 3i)

Detailed Solution: Question 7

(8 - 4i) - (-2 - 3i) + (-10 + 3i)
=> 8 - 4i + 2 + 3i-10 + 3i
=> 8 + 2 - 10 -  4i + 3i + 3i  =>0 + 2i

Test: Introduction To Complex Numbers - Question 8
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Find the multiplicative inverse of  2−3i

Detailed Solution: Question 8

Test: Introduction To Complex Numbers - Question 9
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If (x + iy)1/3 = a + ib, then x/a + y/b = K(a2 − b2), then the value of K is

Detailed Solution: Question 9


Comparing the real and imaginary part on both sides

Test: Introduction To Complex Numbers - Question 10
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If z = 2 − 3i, then z2 − 4z + 13 =

Detailed Solution: Question 10

Test: Introduction To Complex Numbers - Question 11
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Imaginary part of −i(3i + 2) is:

Detailed Solution: Question 11

(-i)(3i) +2(-i) =-3(i^2)-2i =-3(-1)-2i =3-2i since i=√-1 =3+(-2)i comparing with a+bi,we get b=(-2)

Test: Introduction To Complex Numbers - Question 12
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If m1, m2, m3 and m4 respectively denote the moduli of the complex numbers 1 + 4i,3 + i,1 − i and 2 − 3i, then the correct one, among the following is

Detailed Solution: Question 12

Test: Introduction To Complex Numbers - Question 13
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If 2x = 3 + 5i, then what is the value of 2x3 + 2x2 − 7x + 72?

Detailed Solution: Question 13

Test: Introduction To Complex Numbers - Question 14
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Detailed Solution: Question 14

Test: Introduction To Complex Numbers - Question 15
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Evaluate:

Detailed Solution: Question 15

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About this JEE Practice Test

This test contains 15 MCQs on Introduction To Complex Numbers with detailed solutions for each question. It is part of the Mathematics (Maths) for JEE Main & Advanced course on EduRev, designed to align with the current JEE syllabus. Each solution explains not just the correct answer but also gives you an understanding of the topic — not just to attempt the question but also help you prepare for the exam with practice.

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