Complex Numbers JEE Main PYQs PDF, 2020–2026

Complex Numbers questions per year

in the free PDF asked, not in the PDFThe PDF only has questions we can print in full with a checked answer, so it holds 161 of the 162 asked.

Topic-wise weightage by year

How many Complex Numbers questions each topic had in every JEE Main year (all shifts), counting every question asked, including ones not in the PDF. Darker cells mean more questions.

Swipe the table sideways for older years.

Newest questions (2026)

The 12 newest of the 19 JEE Main 2026 Complex Numbers questions in the free PDF, latest shift first.

1. JEE Main 2026 · 8 Apr · Shift 2 · Algebra of Complex Numbers

   The number of values of $z\in {\mathbb{C}}$, satisfying the equations $|z-(4+8i)|=\sqrt{10}$ and $|z-(3+5i)|+|z-(5+11i)|=4\sqrt{5}$, is $:$

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2. JEE Main 2026 · 6 Apr · Shift 2 · Algebra of Complex Numbers

   Let $S=\left\{z\in {\mathbb{C}}:z^{2}+\sqrt{6}iz-3=0\right\}$. Then $\sum_{{z\in S}}z^{8}$ is equal to :

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3. JEE Main 2026 · 6 Apr · Shift 1 · Algebra of Complex Numbers

   Let the set of all values of $k\in {\mathbb{R}}$ such that the equation $z({\bar{z}}+2+i)+k(2+3i)=0,z\in {\mathrm{C}}$, has at least one solution, be the interval $[\alpha,\beta]$. Then $9(\alpha+\beta)$ is equal to:
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4. JEE Main 2026 · 5 Apr · Shift 2 · Algebra of Complex Numbers

   Let $z_{1},z_{2}\in {\mathbb{C}}$ be the distinct solutions of the equation $z^{2}+4z-(1+12i)=0$.

   Then ${|z_{1}|}^{2}+{|z_{2}|}^{2}$ is equal to :

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5. JEE Main 2026 · 5 Apr · Shift 1 · Algebra of Complex Numbers

   Let $a,b\in {\mathbb{C}}$. Let $\alpha,\beta$ be the roots of the equation $x^{2}+ax+b=0$. If $\beta-\alpha=\sqrt{11}$ and $\beta^{2}-\alpha^{2}=3i\sqrt{11}$, then $\left(\beta^{3}-\alpha^{3}\right)^{2}$ is equal to:

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6. JEE Main 2026 · 4 Apr · Shift 1 · Algebra of Complex Numbers

   Let $z$ be a complex number such that $|z+2|=|z-2|$ and arg $\left(\frac{z+3}{z-i}\right)=\frac{\pi}{4}$. Then $|z|^{2}$ is equal to:

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7. JEE Main 2026 · 4 Apr · Shift 2 · Algebra of Complex Numbers

   Let ${\mathrm{S}}=\left\{z\in {\mathrm{C}}:z^{2}+4z+16=0\right\}$. Then $\sum_{{z\in {\ \mathrm{S}}}}|z+\sqrt{3}{\mathrm{i}}|^{2}$ is equal to :

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8. JEE Main 2026 · 2 Apr · Shift 1 · Algebra of Complex Numbers

   Let $x$ and $y$ be real numbers such that $50\left(\frac{2x}{1+3i}-\frac{y}{1-2i}\right)=31+17i,i=\sqrt{-1}$. Then the value of $10(x-3y)$ is :
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9. JEE Main 2026 · 2 Apr · Shift 2 · Algebra of Complex Numbers

   Let the circles $C_{1}:|z|=r$ and $C_{2}:|z-3-4i|=5$, $z\in {\mathbb{C}}$, be such that $C_{2}$ lies within $C_{1}$.
   If $z_{1}$ moves on $C_{1}$, $z_{2}$ moves on $C_{2}$ and $min|z_{1}-z_{2}|=2$, then $max|z_{1}-z_{2}|$ is equal to :

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10. JEE Main 2026 · 28 Jan · Shift 2 · Algebra of Complex Numbers

    Let

    $A=\{z\in {\mathbb{C}}:|z-2|\leq 4\}$ and

    $B=\{z\in {\mathbb{C}}:|z-2|+|z+2|=5\}$.

    Then the max $\{|z_{1}-z_{2}|:z_{1}\in A\text{ and}z_{2}\in B\}$ is :

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11. JEE Main 2026 · 28 Jan · Shift 1 · Algebra of Complex Numbers

    Let $z$ be a complex number such that $|z-6|=5$ and $|z+2-6i|=5$. Then the value of $z^{3}+3z^{2}-15z+141$ is equal to :

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12. JEE Main 2026 · 24 Jan · Shift 2 · Algebra of Complex Numbers

    Let $z=(1+i)(1+2i)(1+3i)\ldots.(1+ni)$, where $i=\sqrt{-1}$. If $|z|^{2}=44200$, then $n$ is equal to $\_\_\_\_$

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