Complex numbers 4

1
Complex numbers 4

• De Moivres Theorem

www.ibmaths.com
2
Who was De Moivre?
A brilliant French mathematician who was
persecuted in France because of his religious
believes. De Moivre moved to England where he
tutored mathematics privately and became friends
with Sir Issac Newton.
De Moivre made a breakthrough in the fields of
probability (writing the Doctrine of Chance), but
more importantly for IB HL students he moved
trigonometry into the field of analysis through
complex numbers with De Moivres theorem.
3
Powers of z.
Make a conjecture for
4
But can we prove it?
Assume n1 the statement is true. Let n k, so
that
Now find
5
So what is the use?
Find an identity for using Mr. De
Moivres fantastic theorey
Remember the binomial expansion
Apply it
Cancel out the imaginery numbers
6
Now try these