Stitz-Zeager_College_Algebra_e-book

117 polar form of complex numbers 843 time to make

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: , we take a step back and think geometrically. We know y = −x describes a line through the origin. As before, r = 0 describes the origin, but nothing else. Consider the equation θ = − π . In this equation, the variable 4 r is free,8 meaning it can assume any and all values including r = 0. If we imagine plotting points (r, − π ) for all conceivable values of r (positive, negative and zero), we 4 are essentially drawing the line containing the terminal side of θ = − π which is none 4 other than y = −x. Hence, we can take as our final answer θ = − π here.9 4 (c) We substitute x = r cos(θ) and y = r sin(θ) into y = x2 and get r sin(θ) = (r cos(θ))2 , or r2 cos2 (θ) − r sin(θ) = 0. Factoring, we get r(r cos2 (θ) − sin(θ)) = 0 so that either r = 0 or r cos2 (θ) = sin(θ). We can solve the latter equation for r by dividing both sides of the equation by cos2 (θ), but as a general rule, we never divide through by a quantity that may be 0. In this particular case, we are safe since...
View Full Document

This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

Ask a homework question - tutors are online