Basic question regarding exponential form

Question

I am currently learning the exponential form of complex numbers. In an example they gave I am having trouble where I marked 1->2. I took the modulus of (1+i) to find r, which gives me 0. How did they get $sqrt{2}$ as the value of r?

Answer 1

I think you might have calculated $\sqrt{1^2+i^2}$ when finding the modulus. This is not the right formula. For a complex number $z=a+ib$, it's modulus is $\sqrt{a^2+b^2}$, so for $z=1+i = 1+1\cdot i$, the modulus is $\sqrt{1^2+1^2}=\sqrt{2}$.