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