1. ## Complex Numbers

To every complex number , z different from -i . assign
f(z) = $\frac{iz}{z+i}$
Denote by M the point of the plane with affix z .
A) a) Find the coordinates of the point B whose affix z0 is the solution of the equation f(z0)= 1 + 2i.
Work !

Affix of B is z0 = xB + iyB
f(z0) = yB = 1 + 2i ..
From the question : Solution : means that if I replace the values I will get zero

To every complex number , z different from -i . assign
f(z) = $\frac{iz}{z+i}$
Denote by M the point of the plane with affix z .
A) a) Find the coordinates of the point B whose affix z0 is the solution of the equation f(z0)= 1 + 2i.
Work !

Affix of B is z0 = xB + iyB
f(z0) = yB = 1 + 2i ..
From the question : Solution : means that if I replace the values I will get zero
So you are asked to solve the equation $\frac{iz}{z+ i}= 1+ 2i$.

Basically, you solve this like you would any equation. Multiply on both sides by z+ i: $iz= (1+2i)(z+ i)= (1+2i)z+ i- 2$. Subtract (1+ 2i)z from both sides: iz- (1+2i)z= (-1- i)z= -2+ i. Divide both sides by -1-i: $z= \frac{-2+ i}{-1-i}$. You can "rationalize" the denominator of that fraction by multiplying both numerator and denominator by the conjugate of -1- i.

3. Thank You -- We solved it in class and You're correct