Do you know what "modulus" and "argument" are? The "modulus" of a complex number, z= a+ bi, is defined as |z|= \sqrt{z\cdot\overline{z}}= \sqrt{a^2+ b^2}. If z= i then \overline{z}= -i so that |i|= \sqrt{i\cdot(-i)}= \sqrt{-(i\cdot i)}= \sqrt{-(-1)}= 1. The "argument" of a complex number, z= a+ bi, is defined as arg(z)= arctan\left(\frac{b}{a}\right). Of course, if z= i, then a= 0 and b= 1 so b/a is not defined. But the tangent function, tan(\theta) goes to infinity as \theta goes to \pi/2 so, "by continuity", the argument of i is pi/2 (your 90 degrees).
Geometrically, if we represent the complex number, z= x+ yi, as a point in the plane, (x, y), then the "modulus" of z is the distance from (x, y) to the origin (0, 0) (just as |x|, with x a real number is the distance on the real-line from x to 0) which is, of course, \sqrt{x^2+ y^2}. And the argument is the angle that line makes with the positive x-axis. Since the "imaginary axis" (y axis) is perpendicular to the "real axis" (x axis) that angle is 90 degrees.
