The Argand diagram represents z=x+yi by the point (x,y), or equivalently by the position vector from the origin. |z|=sqrt(x2+y2). For z 0, the principal argument arg z is measured from the positive real axis and is chosen in (-pi,pi ]. Anticlockwise angles are positive and clockwise angles are negative. Quadrant I Quadrant II Quadrant III Quadrant IV Basic angle, alpha=tan-1| yx|, arg z= alpha,Q1, pi-alpha,Q2, alpha-pi,Q3, -alpha,Q4. **Location** | **Principal argument** Positive real axis | 0 Positive imaginary axis | pi2 Negative real axis | pi Negative imaginary axis | - pi2 Origin | Undefined

The Argand diagram represents \(z=x+yi\) by the point \((x,y)\), or equivalently by the position vector from the origin.

Modulus

For \(z\ne0\), the principal argument \(\arg z\) is measured from the positive real axis and is chosen in \(( -\pi,\pi ]\). Anticlockwise angles are positive and clockwise angles are negative.

\[\text{Basic angle, }\alpha=\tan^{-1}\left|\frac yx\right|,\quad \arg z=\begin{cases}\alpha,&Q1,\\\pi-\alpha,&Q2,\\\alpha-\pi,&Q3,\\-\alpha,&Q4.\end{cases}\]

Argand Diagrams, Modulus and Argument

Argand Diagrams, Modulus and Argument

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