Question

If |z1+z2|>|z1-z2| then prove that -pi/2

Answer 1

. |z1 + z2|<=|z1| + |z2|

|z1 + z2|= square 1.

|z1| + |z2|= square 2.

We have to prove that

square 1

square 2 is true.

Square both sides.

equation

square 3.

2x1x2 +2y1y2 <= square 4

Square both sides again.

2x1x2y1y2 <= x12y22 + y12x22 and we get

0<=(y1x2 - x1y2)2.

It is true because x1, x2, y1, y2 are all real.

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Answer 2

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