Question

express the following complex numbers in the form r(cos theta+i sin theta) 1-sin alpha +i cos alpha where i=iota

Answer 1

A complex number can be visually represented as a pair of numbers (a, b) forming a vector on a diagram called an Argand diagram, representing the complex plane.

"Re" is the real axis, "Im" is the imaginary axis, and i satisfies i2 = −1. A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a solution of the equation x2 = −1.

Because no real number satisfies this equation, i is called an imaginary number. For the complex number a + bi, a is called the real part, and b is called the imaginary part.