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NDA Complex Number PYQs with Solutions

46 previous year questions from Complex Number (NDA Mathematics) with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

46 questionsMathematics2010–2026Answers + solutions

About Complex Number PYQs

Complex Number has 46 previous year questions in the Quantrex Academy NDA Mathematics bank. The 46 questions in this list come from NDA (46), spanning 2010 to 2026. Each question opens on its own page with the options, the correct answer and the worked solution where available.

NDA Complex Number PYQs with Solutions

About Complex Number PYQs

Questions by year (this list)

Complex Number questions with solutions

Consider the following inequalities : I. 1+4i > 3+2i II. 2+3i III. 4+3i > 3+4i where i= -1 How many of the above are valid ?

If p , q , r are the cube roots of unity, then what is vmatrix p^2+q^2 and r^2 and r^2 p^2 and q^2+r^2 and p^2 q^2 and q^2 and r^2+p^2 vmatrix equal to ?

If α , β , γ are cube roots of -8 , then what is (α^2 p^2+β^2 q^2+γ^2 r^2)/(β^2 p^2+γ^2 q^2+α^2 r^2) equal to ?

Let Z_1 and Z_2 be complex numbers such that (3Z_1)/(4Z_2) is purely imaginary. What is |(Z_1+Z_2)/(Z_1-Z_2)| equal to ?

If ω is a non-real cube root of unity, then what is a root of the following equation? vmatrix x+1 & ω & ω^2 ω & x+ω^2 & 1 ω^2 & 1 & x+ω vmatrix = 0

If x + (1)/(x) = 2 θ , then what is x^3 + (1)/(x^3) equal to?

If z ≠ 0 is a complex number, then what is amp(z) + amp( z ) equal to?

If α = -1 + -3 2 , then what is the value of (1 + α^ 19 - α^ 35 )^ 100 - (1 - 3α^ 25 + α^ 38 )^ 50 ?

What is ( 3 +i 3 -i )^3 equal to?

If ((1-i)/(1+i))^ 2m ((1+i)/(1-i))^ 2n = 1 , where i = -1 , then what is the smallest positive value of (m - n) ?

Let 1 , ω , ω^2 be three cube roots of unity. If x = a + b , y = aω + bω^2 , z = aω^2 + bω , then what is x^2 + y^2 + z^2 equal to?

If ω ≠ 1 is a cube root of unity, then what is (1+ω-ω^2)^ 100 +(1-ω+ω^2)^ 100 equal to?

What is the value of the sum ∑_ n=1 ^ 20 (i^ n-1 +i^n+i^ n+1 ) where i= -1 ?

If ω=-(1)/(2)+i 3 2 then what is | array ccc 1+ω & 1+ω^2 & ω+ω^2 1 & ω & ω^2 (1)/(ω) & (1)/(ω^2) & 1 array | equal to?

If x, y and z are the cube roots of unity, then what is the value of x y+y z+z x ?

What is (1+i)^4+(1-i)^4 equal to, where i= -1 ?

If ω ≠ 1 is a cube root of unity, then what are the solution of (z-100)^3+1000=0 ?

Paragraph: Let Z_1 and Z_2 be any two complex numbers such that Z_1^2+Z_2^2+Z_1 Z_2=0 Question: What is the value of (1)/(2)+Re ( Z_1 Z_2 ) ?

If z is any complex number and i z^3+z^2-z+i=0 , where i= -1 , then what is the value of (|z|+1)^2 ?

Let z_1 and z_2 be two complex numbers such that |(z_1+z_2)/(z_1-z_2)|=1 , then what is Re((z_1)/(z_2))+1 equal to?

Paragraph: Let Z_1 and Z_2 be any two complex numbers such that Z_1^2+Z_2^2+Z_1 Z_2=0 Question: What is the value of |(Z_1)/(Z_2)| ?

What is the value of 12+5 i + 12-5 i , where i= -1 ?

If z z =|z+ z | , where z=x+i y, i= -1 then the locus of z is a pair of :

Which one of the following is a square root of - -1 ?

Consider equation-I: z^3+2 z^2+2 z+1=0 and equation -II: z^ 1985 +z^ 100 +1=0 Which of the following is a root of equation-I?

Consider equation-I: z^3+2 z^2+2 z+1=0 and equation -II: z^ 1985 +z^ 100 +1=0 What are the roots of equation – I?

Consider equation-I: z^3+2 z^2+2 z+1=0 and equation -II: z^ 1985 +z^ 100 +1=0 What is the number of common roots of equation-I and equation-II?

If ω is a non-real cube root of 1 , then what is the value of |(1-ω)/(ω+ω^2)| ?

If α and β are the distinct roots of equation x^2-x+1=0 , then what is the value of | α^ 100 +β^ 100 α^ 100 -β^ 100 | ?

If z= 1+i 3 1-i 3 where i= -1 , then what is the argument of z ?

If z is a complex number such that (z-1)/(z+1) is purely imaginary, then what is |z| equal to?

Paragraph: Let z=(1+i θ)/(1-i θ) where i= -1 Question: What is the modulus of z ?

What is the principal argument of (1)/(1+i) where i= -1 ?

Paragraph: Let z=(1+i θ)/(1-i θ) where i= -1 Question: What is angle θ such that z is purely imaginary? where n is an integer

What is the modulus of ( -3 2 -(1)/(2))^ 200 ?

If x^2+x+1=0 , then what is the value of x^ 199 +x^ 200 +x^ 201 ?

What is ∑_ n=1 ^ 8 n+7 i^n equal to, where i= -1 ?

Consider the following statements in respect of the roots of the equation x^3-8=0 : 1. The roots are non-collinear. 2. The roots lie on a circle of unit radius. Which of the above

Which one of the following is a square root of 2 a+2 a^2+b^2 , where a, b ∈ ℝ ? where i= .

If z=x+i y , where i= -1 , then what does the equation z z +|z|^2+4(z+ z )-48=0 represent?

If i= -1 , then how many values does i^ -2 n have for different n ∈ ℤ ?

Consider the following in respect of a complex number Z : 1. (Z^ -1 ) =( Z )^ -1 2. Z Z^ -1 =|Z|^2 Which of the above is/are correct?

The smallest positive integer n for which ((1-i)/(1+i))^ n^2 where i= -1 , is

Consider the following statements in respect of an arbitrary complex number Z : 1. The difference of Z and its conjugate is an imaginary number. 2. The sum of Z and its conjugate

If ω is a complex cube root of unity and x=ω^2-ω-2 , then what is the value of x^2+4 x+7 ?

If x^2+y^2=1 , then what is (1+x+i y)/(1+x-i y) equal to?

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Complex Number in other exams