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Medium Modulus and argument (or amplitude) of a complex number MCQs 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|

Q2MathsUnit 2: Complex Numbers and Quadratic Equations

In the Argand's plane, the locus of

z(\neq

1) such that

\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

\left|\mathbf{z}^{2}-\mathbf{1}\right|=|\mathbf{z}|^{2}+\mathbf{1},

then

\mathbf{z}

lies on

Q4MathsUnit 2: Complex Numbers and Quadratic Equations

Let

z

be a complex number and

c

be a real number

\geq 1

such that

z+

\boldsymbol{c}|\boldsymbol{z}+\mathbf{1}|+\boldsymbol{i}=\mathbf{0},

then

c

belongs to

Q5MathsUnit 2: Complex Numbers and Quadratic Equations

z=\sqrt{\frac{1-i}{1+i}},

then arg

z=

Q6MathsUnit 2: Complex Numbers and Quadratic Equations

z_{1}, z_{2}, \varepsilon C

are such that

\left|z_{1}+z_{2}\right|^{2}=

\left|z_{1}\right|^{2}+\left|z_{2}\right|^{2}

then

\frac{z_{1}}{z_{2}}

Q7MathsUnit 2: Complex Numbers and Quadratic Equations

Calculate all solutions of

|z-1| \times \mid z-

\mathbf{1} \mid=\mathbf{1}

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