If is the point in the argand diagram corresponding to the complex number and if is an isosceles right angled triangle, right angled at , then represents the complex number
Step 1: Finding the value slopes
For the graphical representation of complex numbers, an argand diagram is used, if the complex number is in the form of , in the complex plane. Similar to the x−axis and y−axis in the two-dimensional geometry.
Given the complex number , and is center
Let us draw a figure, according to the question for understanding
The figure shows an Isosceles right-angled triangle
If two lines are perpendicular to each other then the product of their slopes will be equal to , that is
The slope of line OP is
Let , then the slope of line OQ;
Step 2: Substitute the values of slopes into , we get
Step 3: Using the properties of isosceles triangles, Congruent sides of the isosceles triangle are equal, then ,
Use the distance formula between two points , then
Similarly,
Since , then
Put from equation (iii), in the above equation,
Step 4: Substitute in the equation (iii) to find the ordered pair
When , then , and , then ,
Thus, there can be two possible values of are and .
Hence, the answer can be written represents the complex number either or .