Given a circle in the complex plane with a diameter that has endpoints at: -12 − i and 18 + 15i

Find the center of the circle.

Express the following as a function of a single angle, cos(60) cos(-20) - sin(60) sin(-20)

Prove that the sum of two consecutive exponents of the number 5 is divisible by 30.if two consecutive exponents are 5n and 5n + 1, then their sum can be written as 30.

In triangle opq right angled at p op=7cm,oq-pq=1 determine the values of sinq and cosq