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If you are studying maths, you have probably heard of geometry, trigonometry, probability, decimals, equivalent fractions and algebra. If you are above primary school level, you would have of course been taught the **maths basics of addition** and subtraction, multiplication and division. But in all of your studies using numbers *the most surprising maybe* when letters of the alphabet or symbols are introduced into the equation. Like Pi, the golden ratio or proportion, x, y, e, i and the unique algebraic ‘numbers’ of maths.

Maths is such a vast subject to cover and learn, and it starts from basic math to **extremely technical math concepts**. As a student choosing to specialise in mathematics education will understand that to reach the core standard of the course that math practice will be a convenient addition to your life as a mathematician.

Have the skills to **solve math sums** and use your math skills actively to help you to memorise and improve your skills. If you find yourself struggling you can hire a tutor or create a study group with your fellow classmates. A math learning group at school has the common core benefit of allowing you to use math resources that are in your math class including textbooks, and your math teacher if they have time after class as well as joining peers who can work together to improve. This can help you with math questions, to solve problems, it will also make learning a bit more fun plus you benefit from free tutoring.

As you look at the long list of **math problems and advanced math** help that you need. Why not add the number i to the list. Hopefully not for too long as we take a look at it today.

Maths is such a vast subject to cover and learn. Photo Source: Unsplash

The need for i arose from the search for estimations and solutions to non-real equations such as **third-degree equations**. The number I thus is a concept allowing the mathematician to conceive a whole family of square roots in the negative number range.

The number i so-called an **imaginary number and complex number**. It is called an imaginary number because you can not calculate the square root (multiply the value by itself) of negative numbers without producing a positive result. For example, 2² is 4, just like (-2) ².

In mathematics, some equations have no real solution because there is no number whose square root is negative. Therefore complex numbers create the foundation to mix real numbers and imaginary numbers together, **solving these unsolvable problems**. Complex numbers are equations which use the imaginary number i along with real numbers to calculate and solve the unsolvable.

To reinforce this mathematically, we must go back to middle school math class where we learn the basic math rules of the signs such as multiply, subtract, divide or add.

- Imaginary number i looks like this: i, √-1 or j
- Complex numbers look like this: (a+bi)
- Where a = a real number
- Where bi = an imaginary number

- Real numbers and whole numbers look like this: 1, 2, 3
- Negative
**numbers look like this**: -1, -2, -3

In the case of real numbers and imaginary numbers, only numbers from the same family can mix. So, for example, this is a simple, complex number equation.

- (3+2i)+(-1+i) real numbers are in bold font
- Simplified by 1 level is (3+(-1)) + (2i+i)
- Where the calculation begins and the real numbers are brought together to be calculated, and the imaginary numbers go together to be calculated.

- The solution to the top equation is complex number 2+3i
- This can now be plotted on a graph if you decide graphing is the way that you want to display your complex number.

In the 16^{th} century, Girolamo Cardano and Jerome Cardan set out to solve a third-degree equation √-15 And **came upon impossible numbers**. But Raphael Bombelli is the first mathematician to have delved into the mathematical concept and elaborate on the calculation rules. *This is where complex number begin to appear in history, with algebra and impossible numbers*.

- Einstein, the beloved and famous mathematician, used the impossible number and complex number i to build his theory of relativity.
- Rene Descartes, the French philosopher, named the numbers imaginary numbers.
- Leonhard Euler, the co-inventor of the number e (the exponential/infinite number) works with the number i to expand his work on the impossible and imaginary.
- During the 19th century, the number i with the help of authors and mathematicians like CF Gauss. The imaginary number i ends up being accepted as numbers in its own right.
- The number i is used in the common core standards of computation.

use math resources that are in your math class including textbooks. Photo Source: Unsplash

It is true that imaginary numbers, complex numbers, trig. and algebra. Have their place in mathematics, and that **their application may not be useful** for someone who does not study maths. It is also true that this is not the kind of maths that you will find in the kindergarten or primary level classroom.

However, by the time you get to the high school math classroom, there you will find it, discrete and waiting for you. Along with linear equations, differential equations, Pythagorean theorem, triangles, Geometry, Trigonometry, Probability and the mastery of other mathematical concepts.

Oh yes! High school is no joke, and at this grade level, the equations become advanced. **This theorem** will be quite challenging for students who still struggle with arithmetic, subtracting, multiplication problems or average grade math.

As a learner of maths, learning about the number I, should be added to your list of math skills as the use and application of complex numbers are multiple.

However, the learning about complex numbers doesn’t have to be boring, learning fun can go along with even the most challenging maths.

When you are relaxed and have fun, you learn easier, retain knowledge for longer and **not to mention the best part **you enjoy the process. Cool math games were very popular to learn your times tables, calculus adding and subtracting when you were in primary school. *Learning fun with songs, puzzles, perhaps a number jigsaw. At this age, you’ve played, and it became interactive math.*

*The math curriculum gave you a number system, counting, Roun*ding up or down was easy, decimal places, fractions came naturally, then it starts to get more challenging, with number theory and we stop playing. Often we also stop enjoying the math process too. **Just because the curriculum becomes difficult** doesn’t mean that you shouldn’t enjoy learning about maths. Playing a bit each day can help you to excel in your grade level or even surpass the core standards. Remember not all games for kids are exclusively for kids.

Remember not all games for kids are exclusively for kids. Photo Source: Unsplash

- YouTube videos: watching math videos as a part of your online math study can be really engaging and give you a nice break from the books. Often when you watch a few videos,
**you will find a math teacher or math tutor**who explains thing since the way that it clicks in your mind. Helping to bring logic and number sense you what you are studying. Before long it will be as easy as telling time. - Create lesson plans: Making your own study program that splits up the parts that you are struggling with will make it easy to take in. Bite-sized study sessions that are interactive math study sessions with help you to retain what you have learnt. You can use math worksheets, get creative and you’re your own number system, do some puzzles, quizzes…etc.
- Know what you know: review the parts that you have understood quickly every day to refresh and
**build your self-esteem,**and check the math facts as you know - Play online math games: free online math apps are a great way to practice what you know and open your mind up to take in new knowledge.
- If you have a tutor or are a part of a study group be open about where you feel that you need help.
- You can take a specific math course in the area that you need more help in.
- Games: Sudoku is an
**excellent math game from Japan**that is a terrific exercise for the brain. - Sing the multiplication tables: They used to sing as songs in the classroom to help with their memorisation. You can do the same for the math facts of complex numbers.
- Ask for help: leave a note for teachers who tend to be quite creative in their teaching style and ask for tips for maximising your learning.

Have fun with your mathematics, even if your personal study doesn’t follow the curriculum or state standards. You have to do what is best for you to perform at your personal best. Place value on learning these new numbers, they will be a **foundational knowledge **as your maths work gets steadily more challenging.

Read more blogs about special numbers; Pi also Archimedes constant, the famous prime numbers, and the unique perfect numbers.

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