Question

Represent the complex number graphically, and find the trigonometric form of the number.

-2 - 2i

Answer 1

This is what I have so far:


The result will be in Quadrant III.

|a + bi| = sqrt[a2+ b2]
= sqrt[(-2)2+ (-2)2]
= sqrt[4+ 4]
= sqrt[8]
= 2sqrt[2]

r = 2sqrt[2]

tanthetar = |b/a|
theta= [(-2)/(-2)]
tantheta= |1|
theta = tan-1 (1)
theta = 45 degrees

Trigonometric form: 2sqrt[2] [(cos45degrees) + (isin45degrees)]

Answer 2

My teacher said to find a reference angle to 45 degrees. Would I add 180 to 45 to achieve the answer?