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Solve it, - Complex numbers and quadratic equations - JEE Main-10

The point represented by 2+i in the Argand plane moves 1 unit eastwards, then 2 units northwards and finally from there
2\sqrt{2} units in the south-westwards direction.  Then its new position in the Argand plane is at the point represented by

  • Option 1)

     2+2i

  • Option 2)

    1 + i

  • Option 3)

    −1− i

  • Option 4)

    −2−2 i

 
Answers (2)
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N neha

As we have learned

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

 

 

Polar Form of a Complex Number -

z=r(cos\theta+isin\theta)

- wherein

r= modulus of z and \theta is the argument of z

 

 

\left \{ z-(3+3i) \right \}= 2\sqrt2\left (cos (-135\degree)+ i\sin (-135\degree) \right )

= 2\sqrt2(\frac{-1}{\sqrt2}-\frac{i}{\sqrt2})= -2-2i

\therefore -2-2i+3+3i = 1+i

 

 


Option 1)

 2+2i

Option 2)

1 + i

Option 3)

−1− i

Option 4)

−2−2 i

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