Letz

be a complex number that satisfiesz+5z=z+5

Findz.

z +5z* = Z*+5

x + iy +5x - 5yi = x-yi+5

6x - 4yi = SqRt (x+5)^2 + (-y)^2 + 0i -------(1)

therefore -4y = 0 -> y = 0

Sub y into (1) -> 6x = SqRt (x+5)^2

6x = x +5 or 6x = -x-5

5x = 5 x = -5/7

x = 1

when i sub x = -5/7 into the equation, it doesnt sum up, what went wrong?

can you write the full equation for me