Mathematics · JEE

Important Questions: Complex Numbers and Quadratic Equations for JEE

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The most important Complex Numbers and Quadratic Equations questions for JEE cover conceptual traps, standard results, and numerical patterns from Complex numbers as ordered pairs of reals, Representation of complex numbers in the form a+ib and their representation in a plane, Argand diagram, Algebra of complex numbers, and more. Goodmarks provides 46+ high-yield MCQs with full solutions.

Focus on what matters most. These important Complex Numbers and Quadratic Equations questions cover high-weightage concepts from Complex numbers as ordered pairs of reals, Representation of complex numbers in the form a+ib and their representation in a plane, Argand diagram, Algebra of complex numbers, and more — the topics JEE repeats every year.

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Subtopics in Complex Numbers and Quadratic Equations

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Q1MathsUnit 2: Complex Numbers and Quadratic Equations

x+\frac{1}{x}=4,

then

x^{4}+\frac{1}{x^{4}}

is equal to

Q2MathsUnit 2: Complex Numbers and Quadratic Equations

What are the solution(s) to the system of equations

\boldsymbol{y}=\boldsymbol{x}^{2}-\mathbf{9}

and

\boldsymbol{y}-\boldsymbol{3}=

x ?

Q3MathsUnit 2: Complex Numbers and Quadratic Equations

If we plot

\left|Z_{1}\right|=2

and

\left|Z_{2}-6-8 i\right|=4

on the argand plane, the locus of

Z_{1}

and

Z_{2}

are

Q4MathsUnit 2: Complex Numbers and Quadratic Equations

For a complex number z, the minimum value of

|z|+|z-2|

Q5MathsUnit 2: Complex Numbers and Quadratic Equations

A family is going to a theme park having

t

members in the family. Each ticket costs

\$ 80,

and the number of tickets needs to be bought can be calculated from the expression

t^{2}-

4 t-90=6

when

t>0 .

What is the total cost of the theme park tickets that the family paid?

Q6MathsUnit 2: Complex Numbers and Quadratic Equations

(1-i) x+(1+i) y=1-3 i,

then

(x, y)=

Q7MathsUnit 2: Complex Numbers and Quadratic Equations

Determine the nature of roots of the equation

x^{2}+2 x \sqrt{3}+3=0

Q8MathsUnit 2: Complex Numbers and Quadratic Equations

Let

z \neq-i

be any complex number such that

\frac{z-i}{z+i}

is a purely imaginary number. Then

z+\frac{1}{z}

is :

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Frequently asked questions

What makes a Complex Numbers and Quadratic Equations question "important" for JEE?

Important questions test core concepts that appear frequently across JEE Main and Advanced papers — definitions, standard formulas, and classic problem types.

Which subtopics in Complex Numbers and Quadratic Equations are high-weightage?

Key areas include Complex numbers as ordered pairs of reals, Representation of complex numbers in the form a+ib and their representation in a plane, Argand diagram, Algebra of complex numbers, and more. Prioritise these before moving to edge cases.

How many important questions should I revise?

Revise 30–50 important MCQs per unit in the last month before JEE. Focus on questions you got wrong at least once.

Can I practise only important questions on Goodmarks?

Pro users can filter by unit and subtopic to target high-yield areas. Free users can attempt sample questions on this page.