Question

How do I graph the complex number $$2-3i$$ in the complex plane?

Answer 1

Hint: For plotting the complex numbers graphically, we must draw the analogy with the cartesian coordinate system. We must understand the fact that complex numbers $x+yi$ are the same as the point $(x,y)$ . We locate the point $(x,y)$ and then draw an arrow from the origin to the point.

Complete step by step solution:
Complex numbers are a combination of two types of numbers. These two types of numbers are real numbers and imaginary numbers. Real numbers are values of a continuous quantity that can represent a distance along a line. Imaginary numbers are those numbers that are expressed in terms of the square root of a negative number (usually the square root of $-1$ , represented by $i$ or $j$ ). These two numbers make up a complex number. A complex number is represented by the form $a+bi$ where a is the real part and $bi$ is the imaginary part.
When we need to plot the complex number graphically, we can use the cartesian coordinates to plot it. The real number lies along the x axis and the imaginary part lies along the y axis. The behaviour is similar to the coordinates of a point, where the first part is the abscissa and the second part is the ordinate.
Similarly, the given complex number that we have is $$2-3i$$ . This means that the complex number is the point with x coordinate $2$ and the y coordinate is $-3$ .

Note: While plotting the complex number on the argand plane, we must draw an analogy with the cartesian coordinate system. Also, we must take the negative signs in particular very carefully. Also, we must remember to draw the arrow.