 Let us write the complex number z equals negative one plus i in its trigonometric form. It's given in the Cartesian form of the complex number. So we can very quickly see that the real part of z is negative one and the imaginary part of z is positive one. So if we think about that for a moment, right, our x-coordinate is negative, which means we're gonna be over here somewhere, but our y-coordinate is positive. So if you have a negative positive, that puts our point in the second quadrant. That's an important thing to remember here. We compute the modulus, which is gonna be the square root of negative one squared plus one squared. That'll just simplify to be the square root of two. And in terms of the argument, we can make just sort of an arc tangent type argument. We have to do arc tangent of negative one. Now, if you consult your calculator, your calculator, if you take arc tangent of negative one, it wants to give you an angle over here. It's gonna give you negative pi force, but that's an angle in the fourth quadrant. We have to add 180 to it or add pi to it, whichever you're using, gradients or degrees. We have to add pi to that negative pi force. That gives us three pi force, which is an actual angle in the second quadrant. That's why it's important to pay attention to the quadrant. And therefore the trigonometric form of this complex number will be, it always has the form r times cosine theta plus i sine theta. So we plug in the modulus of the square root of two. We plug in the angle, which is three pi force. And we see that z equals the square root of two times cosine of three pi over four plus i sine three pi over four. And I want you to notice here that if we actually computed cosine of three pi force and sine of three pi force, you would end up with negative root two over two plus i times root two over two. If you distribute the square root of two, you're gonna end up with negative two over two plus i times two over two, which simplifies to be negative one plus i. So we can go back from the trigonometric form to the Cartesian form just by computing the trigonometric functions and simplifying it. But we see here how one can write a trigonometric, or how one can write a complex number in trigonometric form.