## Complex numbers

Complex numbers are a group of numbers that help us to get mathematical solutions where real numbers (which includes positive and negative, counting numbers, fractions and decimals) just can’t work. They can be useful in engineering and physical sciences.

They have two parts: one part is an imaginary number. ( For example 3 + 2i) The square of an imaginary number is negative, which is really difficult to imagine!

• CN1 Introduction to complex numbers

What is a complex number? How do we use them with the 4 operations (= - x and ÷) and map them on a plane (which is a 2 dimensional space). Read this pdf to find out and try some questions.

• CN2 Polar form of a complex number

What is a polar complex number? We can identify a complex number on a plane (which is a 2 dimensional space) using rectangular coordinates (e.g. Z = x + Yi ) or we can use polar co-ordinates which involves a length along the x axis followed by an angular rotation θ (e.g. Z=rcisθ).

• CN3 De Moivre's Theorem

What is DeMoivres theorem? De Moivre's theorem gives a formula (formula) to compute the roots or powers of complex numbers. Once the complex number is in polar form, (refer to 'CN2 polar form of a complex number' above) you can calculate its square, cube or higher power. You can also calculate its square root, cube root or other roots.

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