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Mathematics: How are Complex Numbers used in the Real World?

“Being a student is easy. Learning requires actual work.” — William Crawford


Our students come to ME Education to study the curriculums we teach, but they walk away with something far more than the teachings alone. They learn the tools they need to experience the world fully. This is true for all the subjects on offer, even ones that seem difficult to apply to the real world – like complex numbers in Mathematics.

What is a complex number?

In mathematics, simply put, a ‘real’ number, is a value of a continuous quantity that can represent a distance along a line.

An ‘imaginary’ number is a number that, when squared, has a negative result. This means, the number is the square root of a negative number and does not have a tangible value. This is why they are referred to as ‘imaginary numbers.’ They may not be ‘real’ numbers — meaning, they cannot be quantified on the number line, but they are very real in the sense that they exist and are used in mathematics.

Complex numbers are the collection of both ‘real’ numbers and ‘imaginary’ numbers and they are applied to real-life situations every day.

How are Complex Numbers Used?

Imaginary numbers, and the complex numbers they help define, are incredibly useful in the real world. They have a huge impact in physics, engineering, number theory and geometry.

When we measure something that relies on a sine or cosine wave, complex numbers are used. Electricians need them to be able to understand the electricity waves needed in our homes and offices as well as the signals we need on our cell-phones to talk to our friends.

Complex numbers are also used to understand our technological devices because they make up the language of alternating current (AC) electronics. Using imaginary currents, together with real numbers, helps the people who are working with AC electricity, do the calculations while avoiding electrocution.