Modulus is like magnitude. So, in case of complex numbers, we just can’t compare which number is greater and which is smaller, then how come we can say that modulus(magnitude) of ‘i’ is 1?
The modulus of a complex number by definition is given that z = x + iy, then |z| = √(x² + y²), where x and y are real numbers. Modulus is the distance or length of a vector.
Therefore, the modulus of i is
| i | = √(0 + 1²) = √1 = 1
Geometrically, that makes since because you can think of i has a unit vector, so it has unit length of 1.
i=a+bi where a=0 and b=1
use the pythagorean theorem: â(a^2+b^2) which is â1=1