CPM Homework Help : PC Problem 11-70

Find the polar form of the complex number given below. Approximate your values to three decimal places. (Remember to figure out the correct quadrant of the complex number when you find the value for $θ$ .)

$3 − 4i$
Step 1(a):
Graph the point.
Point labeled, a, in fourth quadrant at (3, comma negative 4).
Step 2(a):
Draw a right triangle with the $x$ -axis.
Segments added connecting point to origin, & to (3, comma 0), and from origin to (3, comma 0, area inside triangle shaded.
Step 3(a):
' $r$ ' is the length of the hypotenuse of the triangle. Calculate ' $r$ ' by using the Pythagorean theorem.
Label added to hypotenuse, r.
Step 4(a):
Use trigonometry to find the angle marked $α$ .
Label added to angle opposite vertical leg, alpha.
Step 5(a):
Use the measure of angle $α$ to find $θ$ .
Curved counter clockwise arrow, from positive x axis to hypotenuse, labeled theta.

$−12 − 5i$