How to represent a complex number in the Argand plane?

To represent a complex number in the Argand plane, plot the real part on the x-axis and the imaginary part on the y-axis.

The Argand plane is a graphical representation of complex numbers. It consists of a horizontal x-axis and a vertical y-axis, similar to a Cartesian plane. To represent a complex number in the Argand plane, we plot the real part of the number on the x-axis and the imaginary part on the y-axis.

For example, let's consider the complex number z = 3 + 2i. The real part of z is 3, and the imaginary part is 2. Therefore, we plot the point (3, 2) in the Argand plane.

We can also represent complex numbers in polar form, which involves expressing the number in terms of its magnitude and argument. The magnitude is the distance from the origin to the point representing the complex number, and the argument is the angle between the positive x-axis and the line connecting the origin to the point.

To convert a complex number from rectangular form to polar form, we use the following formulas:

|z| = sqrt(a^2 + b^2)
θ = tan^-1(b/a)

where z = a + bi.

For example, let's consider the complex number z = 3 + 2i again. The magnitude of z is |z| = sqrt(3^2 + 2^2) = sqrt(13), and the argument is θ = tan^-1(2/3). Therefore, we can represent z in polar form as z = sqrt(13) cis(tan^-1(2/3)), where cis denotes the cosine and sine of the argument.

In the Argand plane, we can represent z in polar form by plotting a point at a distance of sqrt(13) from the origin, with an angle of tan^-1(2/3) from the positive x-axis.