### Video Transcript

Express 12 multiplied by cos five
π over six plus π sin five π over six in algebraic form.

This complex number is given in
polar or trigonometric form. It has a modulus of 12 and an
argument of five π over six. When we write a complex number in
algebraic or rectangular form, we write it as π plus ππ, where π is the real
component and π is the imaginary component of this complex number.

We can use these conversion
formulae for converting the polar coordinates with the modulus of π and an argument
of π into the corresponding rectangular form. π is equal to π cos π and π is
equal to π sin π.

Letβs substitute what we know about
our complex number, thatβs π and π, into the conversion formulae. π is equal to 12 multiplied by cos
five π over six, which is negative six root three. π is equal to 12 multiplied by sin
of five π over six, which is six. Now that we have the values for π
and π, we can write our complex number in algebraic form.

Since π is negative six root three
and π is six, our complex number π can be written as negative six root three plus
six π.