I've been struggling with parametrizing things in the complex plane. For example, the circle $|z-1| = 1$ can be parametrized as $z = 1 + e^{i\theta}$. I'm not sure how this was done. I …

Complex Analysis Grinshpan Lines and circles in C Three distinct points z; z1; z2 2 C are on one line whenever the argument of z z1 z z2 is either 0 or ˇ; i.e., the above ratio is real: z z1 z z2 = …

2017年4月30日 · Show that the equation $b(z+\bar z)+\bar b(\bar z-z)+a=0$ represents two straight lines in the complex plane

Show that in $\mathbb{P}^2$, any two distinct lines will intersect in a point. Notice this implies that parallel lines in $\mathbb{C}^2$ , when embedded in $\mathbb{P}^2$ , will intersect at the line …

Putting a Complex Number on a Plane. You may be familiar with the number line: But where do we put a complex number like 3+4i? Let's have the real number line go left-right as usual, and …

2019年3月6日 · Let $\C$ be the complex plane. Let $L$ be a straight line in $\C$. Then $L$ may be written as: $\beta z + \overline \beta \overline z + \gamma = 0$ where $\gamma$ is real …