To solve this, we multiply both the numerator and denominator by the conjugate of the denominator.

The conjugate of (1-2i) is (1+2i).

So, (5+2i)/(1-2i) * (1+2i)/(1+2i)

= (5+2i)(1+2i) / (1-2i)(1+2i) = (5 + 10i + 2i + 4i²) / (1 + 2i - 2i - 4i²)

Since i² = -1, = (5 + 12i - 4) / (1 + 4) = (1 + 12i) / 5

Therefore, in the form a+ib, a = 1/5 b = 12/5

So, (5+2i)/(1-2i) = 1/5 + (12/5)i