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Important Questions: Modulus and argument (or amplitude) of a complex number for JEE

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Part of Complex Numbers and Quadratic Equations in JEE Main Mathematics.

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Q1MathsUnit 2: Complex Numbers and Quadratic Equations
For a complex number z, the minimum value of ∣z∣+∣z−2∣|z|+|z-2| is
Q2MathsUnit 2: Complex Numbers and Quadratic Equations
In the Argand's plane, the locus of z(≠z(\neq 1) such that arg⁡{32(2z2−5z+33z2−z−2)}=2π3is\arg \left\{\frac{3}{2}\left(\frac{2 z^{2}-5 z+3}{3 z^{2}-z-2}\right)\right\}=\frac{2 \pi}{3} i s
Q3MathsUnit 2: Complex Numbers and Quadratic Equations
If ∣z2−1∣=∣z∣2+1,\left|\mathbf{z}^{2}-\mathbf{1}\right|=|\mathbf{z}|^{2}+\mathbf{1}, then z\mathbf{z} lies on
Q4MathsUnit 2: Complex Numbers and Quadratic Equations
Let zz be a complex number and cc be a real number ≥1\geq 1 such that z+z+ c∣z+1∣+i=0,\boldsymbol{c}|\boldsymbol{z}+\mathbf{1}|+\boldsymbol{i}=\mathbf{0}, then cc belongs to
Q5MathsUnit 2: Complex Numbers and Quadratic Equations
If z=1−i1+i,z=\sqrt{\frac{1-i}{1+i}}, then arg z=z=
Q6MathsUnit 2: Complex Numbers and Quadratic Equations
If z1,z2,εCz_{1}, z_{2}, \varepsilon C are such that ∣z1+z2∣2=\left|z_{1}+z_{2}\right|^{2}= ∣z1∣2+∣z2∣2\left|z_{1}\right|^{2}+\left|z_{2}\right|^{2} then z1z2\frac{z_{1}}{z_{2}} is
Q7MathsUnit 2: Complex Numbers and Quadratic Equations
Calculate all solutions of ∣z−1∣×∣z−|z-1| \times \mid z- 1∣=1\mathbf{1} \mid=\mathbf{1}

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

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Key areas include Modulus and argument (or amplitude) of a complex number. Prioritise these before moving to edge cases.

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