Note: When writing complex numbers in trig form, feel free to abbreviate as follows:
Instead of writing out r(cos θ + isin θ), you can just write: r cis θ.

If you go on to more advance mathematics, you will eventually learn about another shortcut notation involving the number e. The notation that I am recommending above is more similar to what you will learn later. The reason, I am not just going ahead and introducing the notation that you will learn about later is becauase it also involves some concepts from calculus that we are not going to get to this semester.

The main advantage to using the r cis θ notation is that it helps to prevent you from making the mistake of using two different angles for θ. If you choose to use the notation in your textbook: r(cos θ + isin θ), please make sure that θ is the same in both the cosine function and the sine function.

Example: It seems that you could represent the number indicated in this graph as 5(cos(π/12) + isin(23π/12)) and numerically, this would work out fine, but don't do it. Instead, write it as 5(cos(23π/12) + isin(23π/12)) or 5(cos(-π/12) + isin(-π/12)) or you can use some other angle associated with the same terminal side as the standard angle -π/12. The point here, is that the angle in the complex number representation should represent the standard angle when the point is graphed.

If you just write this point as 5cis(-π/12) or 5cis(23π/12), you eliminate the possibility of using two different angles.