How it works: In this base, digits represent different powers of 7i. 7i to the power of 0 is equal to 1. 7i to the power of 1 is equal to 7i. 7i to the power of 2 is equal to –49. 7i to the power of 3 is equal to –343i and so on. This creates a pattern where we have a positive real number, then positive imaginary number, then negative real number, then negative imaginary number, and then again positive real number. But what digits should we use in this base? In base square root of 5 we used the same digits as in base 5. 7i is equal to the square root of –49, so in this base we will use the same digits as in base –49, that is from 0 to [48]. This allows us to express any real and any imaginary number. But this base also allows us to represent numbers that have both the real part and the imaginary part. For example, 72 in this base is equal to 49i + 2.
C2A.
