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Complex Numbers - Cambridge Question (1 Viewer)

shaon0

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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
 

Drongoski

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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.
 

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