How do we represent complex numbers, their conjugate, modulus and argument of a complex numbers in argand plane?

Question

Ethan Adkins · Accepted Answer

Please see below.

Argand Plane is a plot of complex numbers as points on a two dimensional complex plane using #x#-axis as the real axis and #y#-axis as the imaginary axis.

In this plane every complex number, say #x+iy#, is represented by a point. Its reflection in real axis i.e. #x#-axis represents its conjugate complex number.

We can add two numbers by joining the two points representing the two numbers to #0+i0# (equivalent of origin) and then completing the parallelogram.

The length of line joining the number is its absolute value also known as modulus and the angle, this line makes with positive side of real axis or #x#-axis is known as argument of the number.

The number appears as:

Abigail Allen · Answer

undefined Complex numbers are represented in the Argand plane, which is a two-dimensional coordinate system. In this plane, the real part of a complex number is represented on the x-axis, while the imaginary part is represented on the y-axis.

The conjugate of a complex number is obtained by changing the sign of its imaginary part. For example, if a complex number is represented as a + bi, its conjugate would be a - bi.

The modulus (or absolute value) of a complex number is the distance between the origin and the point representing the complex number in the Argand plane. It can be calculated using the formula |z| = √(a^2 + b^2), where a and b are the real and imaginary parts of the complex number, respectively.

The argument (or angle) of a complex number is the angle between the positive x-axis and the line connecting the origin and the point representing the complex number in the Argand plane. It can be calculated using the formula θ = tan^(-1)(b/a), where a and b are the real and imaginary parts of the complex number, respectively.

In summary, complex numbers are represented in the Argand plane, their conjugate is obtained by changing the sign of the imaginary part, the modulus is the distance between the origin and the point representing the complex number, and the argument is the angle between the positive x-axis and the line connecting the origin and the point representing the complex number.