# Formulas of Complex Numbers

Shortcut tricks on formulas of complex numbers are one of the most important topics in exams. Competitive exams are all about time. If you know time management then everything will be easier for you. Most of us miss this thing. We provide examples on Formulas of Complex Numbers shortcut tricks here in this page below. All tricks on formulas of complex numbers are provided here. We request all visitors to read all examples carefully. These examples here will help you to better understand shortcut tricks on formulas of complex numbers.

Before starting anything just do a math practice set. Choose any twenty math problems and write it down on a page. Using basic math formula do first ten maths of that page. You also need to keep track of the time. After finish write down total time taken by you to solve those ten maths. Now go through our page for formulas of complex numbers shortcut trick. After finishing this do remaining questions using Formulas of Complex Numbers shortcut tricks. Again keep track of the time. The timing will be surely improved this time. But this is not all you want. You need to practice more to improve your timing more.

### Few Important things to Remember

Math section in a competitive exam is the most important part of the exam. That doesn’t mean that other sections are not so important. But if you need a good score in exam then you have to score good in maths. You can get good score only by practicing more and more. You should do your math problems within time with correctness, and this can be achieved only by using shortcut tricks. Again it does not mean that you can’t do maths without using shortcut tricks. You may have that potential that you may do maths within time without using any shortcut tricks.

But, so many other people may not do the same. Here we prepared formulas of complex numbers shortcut tricks for those people. We try our level best to put together all types of shortcut methods here. But, we may miss few of them. If you know anything else rather than this please do share with us. Your help will help others.

### Definition:

i = √-1 and i^{2} = -1, i^{3} = i^{2 }.i = -i,

then,

i^{4} = i^{3} . i = -i . i = 1,…i^{4n} = 1,

and,

i^{4n+1} = 1, i^{4n+2} = -1, i^{4n+3} = -i

**Complex number is any number of the form a + bi and where as a and b are real number.**

### Formulas of Complex Numbers

**Addition:** (a + bi) + (c + di) = (a + c) + (b + d)i

**Subtraction :** (a + bi) – (c + di) = (a – c) + (b – d)i

**Multiplication :**(a + bi)(c + di) = ac + adi + bci + bdi^{2} = (ac – bd) + (ad + bc)i

**Multiplying Conjugates :** (a + bi)(a – bi) = A^{2} + b^{2}

**Division :** a + bi / c + di = a + bi / c + di x c – di / c – di = ac + bd / c^{2} + d^{2} + (bc – ad / c^{2} + d^{2})i

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