and are complex numbers in argand diagram and is the origin.
show and are perpendicular if
Hello, stud_02!
How about a geometric proof?
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: .
Hello again, stud_02!
An algebraic proof is probably expected . . .
Let: .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.