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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.

Knowledge of these complex numbers also allows us to keep using smaller devices with even more power, simply because the manufacturers understand the language of transistors and microchips – thanks to complex number application.

Other things that require the understanding of complex numbers, include the wireless technology we all rely on for our internet access and even interpreting the scans doctors perform in hospitals.

Complex numbers are used a lot in the study of quantum physics. They help scientists to model periodic motions like water and light waves. Understanding complex numbers helps countries keep its citizens safe by being able to interpret data around how earthquakes shake buildings thereby understanding how to build structurally sound buildings. They even help us to know if we should wear a raincoat when we go outside as the weather forecasters use mathematical theories on which the forecasting models are based. Complex numbers creep into pretty much every avenue of our modern lives. In fact, without using them to calculate various circuit theories, you would not be able to read this very blog on a computer.

Cambridge IGCSE Mathematics

All of these exciting applications can only be harnessed once we understand the theory behind these complex number systems. Our students are given an appropriate introduction in the Cambridge IGCSE Mathematics curriculum which combines knowledge and skills to give students a solid foundation for further study.

From Cambridge IGCSE Mathematics, students can progress to Cambridge IGCSE Additional Mathematics or straight to Cambridge International AS & A Level Mathematics, or other qualifications at that level.

Cambridge IGCSE is accepted at leading universities and it opens the door to careers around the world.

To learn more about our Mathematics offerings, please contact us at 2383 0300.


"I planned to apply to schools in the UK, but my grades were not doing so well, especially with A-Level Mathematics, Biology, Chemistry, and Physics. A friend referred me to ME Education. I heard their A-Level subject tutoring is amazing! I joined the ME Education UK exam prep program on F.4 and stayed for two and half years with Mr. Andy and Mr. Adeel. I decided to study Medical & Dental programs in the UK, so I reached out to ME & Aspire partnership and received so much expert university admissions guidance from Real Doctors & Dentists. They provided me Personal Statement Coaching, Entrance Exam Training, and MMI Interview prep. ME also helped me apply to the right school, and finally, I got into King's College London! After moving to the UK, teachers at ME are continuing to mentor me online and make sure I am keeping up with the school. I can't thank ME Education enough for helping me to achieve my educational goal!"



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