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Further Mathematics
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Prove e^(ix) = cos (x) + isin(x)

We first write each side of the equation using the maclaurin series for each function.

eix = 1 + ix + (ix)2/2! + (ix)3/3! + (ix)4/4! + ......

PM
7006 Views

What does it mean if two matrices are said to be commutative?

Two matrices are commutative is matrix A multiplied by matrix B equals matrix B multiplied by matrix A.

JM
5677 Views

What is differentiation used for?

Differentiation is used to find the gradient of a line, or curve. It can also be used to find the co-ordinates of stationary points, whether these be minimum, maximum or points of inflection. The secon...

JM
9564 Views

How do you find the square roots of a complex number?

Every complex number has complex square roots. However since we don't know how to deal with expressions such as √i we need to follow a specific method to find the square roots of a complex number.<...

JG
66592 Views

Are we able to represent linear matrix transformations with complex numbers?

Absolutely. Consider a point (a,b). This may be represented by the complex number a+bi and also by the column vector (a;b), where the semicolon means 'new line'.
To translate the point by +(c,d), in ...

JO
3568 Views

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