### Video Transcript

Given that π§ one is equal to five
multiplied by cos two π plus π sin two π and π§ two is equal to a quarter
multiplied by cos four π plus π sin four π, find π§ one π§ two.

Recall the product formula. This says that, for two complex
numbers expressed in polar form, π§ one has a modulus of π one and an argument of
π one and π§ two which has a modulus of π two and an argument of π two, their
products can be found by multiplying together their moduli and adding together their
arguments. Itβs π one π two multiplied by
cos of π one plus π two plus π sin of π one plus π two.

In our question, the modulus of π§
one is five and the modulus of π§ two is one-quarter. This means we can find the modulus
of π§ one π§ two by multiplying five by one-quarter, which is five-quarters. The argument of π§ one is two π,
and the argument of π§ two is four π. So, we find the sum of their
arguments. Thatβs two π plus four π, which
is six π. π§ one π§ two is therefore given as
five-quarters multiplied by cos six π plus π sin six π.