If you want to get real nerdy about it this works because the natural logarithm of 2 is ~0.69

(1+i)^n = 2

n log (1+i) = log 2

n = log 2 / log (1+i)

For small numbers, log(1+x) ≈ x

n ≈ log 2/i

log 2 ≈ 0.69

n ≈ 0.69 / i

n ≈ 69/100i

Which is pretty close to 70/100i which is the approximation.