Find the modulus and argument of the complex number 1+2i

It is always helpful to start by drawing a diagram with a Real and Imaginary axis then plotting the number (in our case 1+2i) on the diagram and drawing a line from the origin to our point. Remember the modulus tells us the distance between our point and the origin, and the argument gives us the angle between our number and the positive real axis. To find the modulus, which we will call r, we can use Pythagoras theorem: a^2 + b^2 = c^2. So, we can see that r^2 = 1^2 + 2^2 and therefore r= sqrt(2). To find the argument we want to find the angle theta from the real axis to our point, so we need to use SOH CAH TOA. Since we know the length of the Opposite side and the Adjacent side, we can use that tan(theta) = Opposite/Adjacent. Just use the inverse of tan to obtain theta. i.e. theta = arctan(Opposite/Adjacent),