Complex number question help! (1 Viewer)

[So-smart]

If |z1 -z2| = |z1 + z2| show that arg z1 -arg z2 = pi/2

Please help, and give ur working out.

Thanks in advance.

 

[So-smart]

PLEEEASSSEE!! this assignment is due tommorrow and i m stuck on this question!! PLEASE help...

 

[cutemouse]

Maybe you could start by posting it in the correct section? lol

 

[So-smart]

I would..if i knew how to....if u haven't looked already i am a new member..

 

[kwabon]

not sure whether the working is right but here goes,

{ z1 - z2 } = { z1 + z2 }

therefore it is a rectangle
therefore all angles in a rectangle are 90 degrees
therefore arg z1 - arg z2 = 90 degrees

pop in a nice little sketch on z1 and z2
z1 being in the first quadrant and z2 being in the second quadrant with the same y value and there u go

hehehe
its prolly not right (the working out)

hope it helped

 

[Trebla]

Use a geometric interpretation. The equality of the moduli indicates vector(z₁ - z₂) has equal length to vector(z₁ + z₂). Both vectors represent the diagonals of a parallelogram. However since they are of equal length, this suggests it's a special parallelogram, namely a rectangle, hence you can deduce the difference in arguments to be a right angle.

 

[Iruka]

Don't they need to be non-zero?

 

[So-smart]

Thanks guyz...but i already gave in my assignment , thanks for taking the time to answer my question.