How do you write the trigonometric form of #1+6i#?
Converting complex numbers into trigonometric form is very similar to converting rectangular coordinates (aka Cartesian Coordinates) into polar coordinates. There are 2 formulas that will assist (assuming the complex number is in
We begin by finding the value
Next, we can determine the reference angle. For this problem, I am using degrees, though the same work could be done with radians as the measure instead.
This is only the reference angle, which will always be in the first quadrant when done this way. The complex number
The trigonometric form of a complex number
Thus, our answer is: