How do you represent complex numbers in Argand diagrams?

How do you represent complex numbers in Argand diagrams?

Another name for an Argand diagram is the complex plane. So, a complex number like Z = 3 + 4i would have the coordinates (3, 4) on an Argand diagram. Note the horizontal axis is labelled Real{Z} and the vertical axis is labelled Imag{Z} where the word Imaginary has been shortened to Imag.

How do you sketch a graph with complex numbers?

How To: Given a complex number, represent its components on the complex plane.

1. Determine the real part and the imaginary part of the complex number.
2. Move along the horizontal axis to show the real part of the number.
3. Move parallel to the vertical axis to show the imaginary part of the number.
4. Plot the point.

How are complex numbers multiplied?

Multiplying a complex number by a real number (x + yi) u = xu + yu i. In other words, you just multiply both parts of the complex number by the real number. For example, 2 times 3 + i is just 6 + 2i. Geometrically, when you double a complex number, just double the distance from the origin, 0.

How do you calculate complex numbers?

Sums of Complex Numbers This is done by adding the corresponding real parts and the corresponding imaginary parts. For example, the sum of 2+3i 2 + 3 i and 5+6i 5 + 6 i can be calculated by adding the two real parts (2+5) and the two imaginary parts (3+6) to produce the complex number 7+9i 7 + 9 i .

How to plot complex numbers on an Argand diagram?

An Argand Diagram is a plot of complex numbers as points. The complex number z = x + yi is plotted as the point (x, y), where the real part is plotted in the horizontal axis and the imaginary part is plotted in the vertical axis. The following diagram shows how complex numbers can be plotted on an Argand Diagram.

What do the intersecting lines on an Argand diagram represent?

The intersecting lines represent the location of the complex number. Another name for an Argand diagram is the complex plane. So, a complex number like Z = 3 + 4i would have the coordinates (3, 4) on an Argand diagram.

How do you find the complex conjugate pair in an Argand diagram?

Example 4: Identify the complex number for each of the points in the Argand diagram. Z A and Z B are a complex conjugate pair because of their symmetry about the real axis. Z A = -7 + 4i while Z B = -7 – 4i.

What is the difference between Cartesian and Argand diagram?

Analogous to the Cartesian plane is the Argand diagram, also called the complex plane, where the horizontal axis is the real part of a number and the vertical axis is the imaginary part. Numbers which have a real part and imaginary part are called complex numbers.