Complex Numbers - Cambridge Question (1 Viewer)

[ashokkumar]

If |z1 + z2| = |z1 - z2|, find the possible values of arg(z1/z2)

 

[shaon0]

arg(z1/z2)=arg(z1)-arg(z2)
1) Construct a parallelogram using z1 and z2
2) Now the diagonals of theis parallelogram have to be equal
3) Only parallelogram with equal diagonals are: square, rectangle and rhombus
4) Drawing a rectangle, square and/or a rhombus makes the solution obvious
Thus, arg(z1/z2)=+-pi/2

 

[untouchablecuz]

 

[Drongoski]

arg(z1/z2)=arg(z1)-arg(z2)
1) Construct a parallelogram using z1 and z2
2) Now the diagonals of theis parallelogram have to be equal
3) Only parallelogram with equal diagonals are: square, rectangle and rhombus
4) Drawing a rectangle, square and/or a rhombus makes the solution obvious
Thus, arg(z1/z2)=+-pi/2

Apart from a square, a rhombus has unequal diagonals.

 

[ashokkumar]

thanks a lot guys