and are complex numbers in argand diagram and is the origin.

show and are perpendicular if

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- May 13th 2009, 04:38 AMstud_02complex numbers
and are complex numbers in argand diagram and is the origin.

show and are perpendicular if

- May 13th 2009, 08:26 AMSoroban
Hello, stud_02!

How about a geometric proof?

Quote:

and are complex numbers in argand diagram and is the origin.

Show and are perpendicular if: .

Code:`Q * - - - - - - - - - - - * R`

/ * * /

/ * * /

/ * * /

Z2 / * /

/ * * /

/ * * /

/ * * /

O * - - - - - - - - - - - * P

Z1

Then: .

Hence .

If , then: .

. . And we have a parallelogram with equal diagonals.

A parallelogram with equal diagonals is a.*rectangle*

. . Therefore: .

- May 13th 2009, 05:47 PMSoroban
Hello again, stud_02!

An algebraic proof is probably expected . . .

Quote:

and are complex numbers in the argand diagram and is the origin.

Show if

We know that: .

. . That is: . .[1]

We will show that [1] is true.

. .

. .

Since , we have: .

Square both sides: .

Expand: .

. . which simplifies to: . . Q.E.D.

- May 13th 2009, 06:29 PMpankaj