 # Complex Numbers with Vector Addition

Complex Numbers with Vector Addition is obtained using the sides of triangles, the sum of sides of two sides of a triangle is greater than the other side. Worked Examples of Complex Numbers with Vector Addition Suppose $\displaystyle 0 \lt \alpha, \ \beta \lt \frac{\pi}{2}$ and define complex numbers $z_n$ by z_n = [...] # Locus of Complex Numbers

Locus of Complex Numbers is obtained by letting $z = x+yi$ and simplifying the expressions. Operations of modulus, conjugate pairs and arguments are to be used for determining the locus of complex numbers. Worked Example of Locus of Complex Numbers Let $z = x + iy$ be a complex number such [...] # Complex Number Regions

Regions defined by complex numbers $\displaystyle z = x + yi$ where $x$ and $y$ are real numbers, can be drawn using inequalities for complex number regions. Worked Example of Complex Number Regions Find the inequality of complex region $\displaystyle \Bigg|1+\frac{1}{z}\Bigg| \le 1$. Show Solution \( \begin{aligned} \displaystyle \require{color} \frac{|z+1|}{|z|} &\le [...]