 In this video, we provide the solution to question number 11 from the practice final exam for math 1060, in which case we're supposed to find the modulus and argument of the complex number z equals one plus i. I should point out that finding the modulus and argument for a complex number is equivalent to converting a Cartesian point into polar coordinates. It's also equivalent to finding the geometric representation of an algebraic vector. So we've done this problem many times with just different flavors, so to speak. So we have this complex number, whose real part and imaginary part are both one. And so in terms of finding the argument with the length of the vector, this thinking the complex number as a vector, we see that the absolute value of z is gonna equal the square root of one square plus one squared. So we get the square root of two. So we can see that some of these answers can be eliminated pretty quickly because only a, e, and c have the square root of two because the correct modulus. What about the angle? Well, we get that the angle tangent theta is gonna equal y over x here, the real imaginary parts of one over one equals one. So when does tangent equal one? Well, that happens when sine and cosine are the same. So we're gonna get that theta equals, well, tangent equals one at 45 degrees. Also, it'll equal that at 225 degrees. But what quadrant are we in? Positive, real part, positive imaginary part. So we're in the first quadrant here. So we're looking for 45 degrees. JK, we should always be doing radians here, of course. So pi fours would be the correct argument. And so we see that the correct choice is a.