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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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