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## Homework Statement

Question:

## Homework Equations

Any relevant to complex numbers.

## The Attempt at a Solution

Given,

Arg([itex]\frac{z}{w}[/itex])= Arg(z)-Arg(w)

z=x+yi

z

_{1}= -1-2i

z

_{2}= 2+3i

Arg(z-z

_{1})=Arg(z

_{2}-z

_{1})

LHS:

Arg(x+yi+1+2i)

Arg((x+1) + i(y+2))

tan([itex]\theta[/itex])=[itex]\frac{y+2}{x+1}[/itex]

RHS

Arg(2+3i+1+2i)

Arg(3+5i)

tan([itex]\theta[/itex])=[itex]\frac{5}{3}[/itex]

RHS = LHS

[itex]\frac{y+2}{x+1}[/itex] = [itex]\frac{5}{3}[/itex]

Simplified

y = [itex]\frac{5}{3}[/itex]x -[itex]\frac{1}{3}[/itex]

Is this right?