Write the complex number in trigonometric form, once using degrees and once using radians. Begin by sketching the graph to help find the argument θ. (Do not use cis form.)
$$−1 + i$$
My work:
I graphed $x = -1$ and $y = 1$
$$z=r= \sqrt{ x^2 + y^2}$$
$$r= \sqrt{2}$$
$$\tan \theta = \frac{Opposite}{Adjacent} $$
$$\tan \theta = \frac{-1}{1} = -1$$
$$\theta= 45^\circ$$
When put into trig form: $$\sqrt{2} (\cos 45^\circ +i \sin 45^\circ)$$
Here is how my submitted answer looks (it is #9): http://i.imgur.com/hrrg6hg.png
I also need help with $9 − 40i$ (instructions: convert the complex number to trigonometric form. (Enter the angle in degrees rounded to two decimal places. Do not use cis form.).
I went through the same steps as I did on the other problem, and I got $r=41$ and $θ= -77.32$.
Best Answer
You have that:$x = - 1, y = 1, z = x+iy \Rightarrow \theta = \pi+\tan^{-1}\left(\dfrac{y}{x}\right) = \pi+\tan^{-1}(-1) = \pi+\dfrac{-\pi}{4}=\dfrac{3\pi}{4}, r= \sqrt{x^2+y^2}=\sqrt{2}$