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  • Solve it, - Complex numbers and quadratic equations - JEE Main-3

If z= 2+i is reflected twice in order, firstly in real axis then in imaginary axis then the resulting complex number z_{1}

  • Option 1)

    lies in 1st quadrant with z_{1}= 2+i

  • Option 2)

    lies in 2nd quadrant with z_{1}= -2+i

  • Option 3)

    lies in 3rd quadrant with z_{1}= -2-i

  • Option 4)

    lies in 4th quadrant with z_{1}= 2-i

 

Answers (1)

 

From fraph we see, after 1st reflection in real axis Z reaches 2nd quad at (2-i) then after 2nd reflection in imaginary axis it reaches 3rd quadrant at Z_{1} =-2-i

 

Representation of complex number in Argand plane (Similar to Cartesian plane) -

z=x+iy is represented on a plane similar to cartesian plane with horizontal line as real axis and vertical as imaginary axis.  z=x+iy  on plane will be a point with co-ordinate (x,y).

- wherein

x will be taken along real axis and y will be taken along imaginary axis. x will increase from left to right & y will increase from bottom to top. Point of intersection of both axis will have co-ordinate (0,0) for complex number z=0

 

 


Option 1)

lies in 1st quadrant with z_{1}= 2+i

This is incorrect

Option 2)

lies in 2nd quadrant with z_{1}= -2+i

This is incorrect

Option 3)

lies in 3rd quadrant with z_{1}= -2-i

This is correct

Option 4)

lies in 4th quadrant with z_{1}= 2-i

This is incorrect

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