Complex Numbers

Complex numbers are used throughout mathematics in order to allow manipulation of numbers which may not be real as such. This results in the imaginary number root -1.

Imaginary numbers, denoted by the letter I, allow for an algebraic form to take place so we can use imaginary numbers in what ever way we please.

Complex numbers combine a real and imaginary part and are denoted by z. Therefore, a complex number is in the form z = a + bi, where ‘a’ and ‘b’ are real numbers and ‘i’ is the imaginary number root -1.

Complex numbers can be represented on an argand diagram where along the x-axis we have the number line and along the y-axis we have the imaginary number line:


From this we can work out the modulus of this complex number which in a sense is the length. This is denoted by the modulus lines: |z|. The argument is the angle in which the complex number ‘z’ gives from the x-axis and origin (in radians):


Complex Numbers in Industry

Complex numbers are used everywhere in industry and in more places than you may think. For example, in physics and electrical engineering they are used in oscilloscope oscillations and in measuring alternating current and signals.

Also they are used in mathematical research in numerical analysis but also through electrostatics and fluid dynamics.


Complex numbers are everywhere and I hope this gives you a small insight into where they come from and where they’re used. Next I will be looking at matrices and how we can use these to our advantage.

Keep Learning!

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