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One root of (1)^{\frac{1}{3}}  is:

  • Option 1)

    \frac{\sqrt 3 i}{2}

  • Option 2)

    \frac{1+\sqrt 3 i}{2}

  • Option 3)

    \frac{1-\sqrt 3 i}{4}

  • Option 4)

    \frac{-1-\sqrt 3 i}{2}

 

Answers (1)

best_answer

As we learnt in 

Definition of Complex Number -

z=x+iy, x,y\epsilon R  & i2=-1

- wherein

Real part of z = Re (z) = x & Imaginary part of z = Im (z) = y

 

 As learnt in concept

Definition of Complex Number -

z=x+iy, x,y\epsilon R  & i2=-1

- wherein

Real part of z = Re (z) = x & Imaginary part of z = Im (z) = y

 

 \\ \left ( 1 \right )^{\frac{1}{3}}=x\\*\\*x^{3}-1=0\\*\\*\left (x-1 \right )\left (x^{2} +x+1 \right )=0\\*\\*x=\frac{-1\pm \sqrt{3}i}{2}


Option 1)

\frac{\sqrt 3 i}{2}

Incorrect

Option 2)

\frac{1+\sqrt 3 i}{2}

Incorrect

Option 3)

\frac{1-\sqrt 3 i}{4}

Incorrect

Option 4)

\frac{-1-\sqrt 3 i}{2}

Correct

Posted by

divya.saini

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