# How do you use the binomial theorem to expand #(5-sqrt3i)^4#?

##### 1 Answer

#### Explanation:

Since you asked how to use the binomial theorem for this question, here goes:

The binomial theorem says that an expression of two terms added or subtracted raised to a power

Therefore,

Simplifying this you get:

Ultimately leading down to:

On a side note, this question is probably easier to attempt using de Moivre's theorem, which states that

Let

Therefore,

To find

Therefore

So,

Then, re-convert back into Cartesian form.

Obviously this is only handy if you have a calculator on hand to crunch the numbers. You get the same result as above, but it's up to you which method you use.