Please be careful with two different things. Complex numbers have two components. Distances don’t. They are scalars. The length of the vector (0,1) is also 1. Just as a+bi will have the length sqrt(a^2 + b^2). You can also use polar coordinates for complex numbers. This way, you can see that i has length 1, which is the distance from 0.
The triangle in the example above adds a vector and a scalar value. You can only add two vectors: (1,0) + (0,1) which results in (1,1) with the proper length. Or you can calculate the length/distance (absolute values) of the complex numbers directly.
Please be careful with two different things. Complex numbers have two components. Distances don’t. They are scalars. The length of the vector
(0,1)is also1. Just asa+biwill have the lengthsqrt(a^2 + b^2). You can also use polar coordinates for complex numbers. This way, you can see thatihas length1, which is the distance from0.The triangle in the example above adds a vector and a scalar value. You can only add two vectors:
(1,0) + (0,1)which results in(1,1)with the proper length. Or you can calculate the length/distance (absolute values) of the complex numbers directly.