1. Complex Numbers #2

Hi

The question says:
Find the Argument of z for each of the following in the interval [2,2pi]

A) Z=1-√3i

B) Z=-√7

C) Z=55

D) -2-2√3i

please help i dont understand the method for solving this, i got a worked example but i dont understand it, can any please explain the process of solving.

thnx

2. Originally Posted by iFuuZe
Hi

The question says:
Find the Argument of z for each of the following in the interval [2,2pi]

A) Z=1-√3i

B) Z=-√7

C) Z=55

D) -2-2√3i

please help i dont understand the method for solving this, i got a worked example but i dont understand it, can any please explain the process of solving.

thnx

The argument of a complex number $\displaystyle z=x+iy\,,\,\,x,y\in\mathbb{R}\,,\,x\neq 0$ is given by $\displaystyle arg(z):=\arctan(y/x)$ , choosing

the angle depending on the signs of $\displaystyle x,y$.

Thus, for example, $\displaystyle arg(1+i\sqrt{3})=\arctan\sqrt{3}=\frac{\pi}{3}$ , whereas $\displaystyle \arg(-1-\sqrt{3})=\arctan\sqrt{3}=\frac{4\pi}{3}$

Tonio