Distance Formula Using Complex Numbers

Q.

Find area of the triangle whose vertices are $\left(2,3\right),\left(-1,0\right)$ and $\left(2,-4\right)$

Q.

The points $(0,5),(0,-9)$ and $(3,6)$ are collinear. State whether the following statement is true or false. Justify your answer.

1. True
2. False

Q. If A, B, C are represented by 3 + 4i, 5 - 2i , -1 + 16i, then A, B, C are
[RPET 1986]

1. Collinear

2. Vertices of equilateral triangle

3. Vertices of isosceles triangle

4. Vertices of right angled triangle

Q. If $\left|\frac{z-2}{z-3}\right|=2$ represents a circle whose radius is $r$, then the value of $3r$ is

Q. If $b+ic=(1+a)z$ and $a^2+b^2+c^2=1,$ where $a,b,c\in R,$ then $\frac{1+iz}{1-iz}=\frac{a+ib}{k}$ where $k$ is equal to

1. $1+a$
2. $1+b$
3. $1+c$
4. $2+b$