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Tell me? - Complex numbers and quadratic equations - JEE Main-12

The complex number $z$ satisfying $\left |z \right |= 2$  will be

• Option 1)

$z= 1+i$

• Option 2)

$z= \sqrt{3}-i$

• Option 3)

$\sqrt{2}+i$

• Option 4)

$z= 1-i$

Answers (1)
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if $z=1+i$, then $\left |z \right |=\sqrt{1^{2}+1^{2}}=\sqrt{2}$

if $z=\sqrt{3}-i$, then  $\left |z \right |=\sqrt{\left (\sqrt{3} \right )^{2}+\left (-1 \right )^{2}}=\sqrt{3+1}=2$

if $z=\sqrt{2}+i$, then  $\left |z \right |=\sqrt{\left (\sqrt{2} \right )^{2}+1^{2}}=\sqrt{2+1}=\sqrt{3}$

if $z=1+i$ then  $\left |z \right |=\sqrt{1^{2}+\left (-1 \right )^{2}}=\sqrt{1+1}=\sqrt{2}$

$\therefore$ Option (B)

Definition of Modulus of z(Complex Number) -

$\left | z \right |=\sqrt{a^{2}+b^{2}}$ is the distance of z from origin in Argand plane

- wherein

Real part of z = Re (z) = a & Imaginary part of z = Im (z) = b

Option 1)

$z= 1+i$

This is incorrect

Option 2)

$z= \sqrt{3}-i$

This is correct

Option 3)

$\sqrt{2}+i$

This is incorrect

Option 4)

$z= 1-i$

This is incorrect

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