b). find e rate values of a anb ine 13. sqrt(a+bi) = 2+3i

$$\sqrt{a+bi} = 2+3i$$ $$(\sqrt{a+bi})^2 = (2+3i)^2$$ $$a+bi = (2+3i)(2+3i)$$

$$a+bi = 2(2) + 2(3i) + 3i(2) + 3i(3i)$$ $$a+bi = 4 + 6i + 6i + 9i^2$$

Since $i^2 = -1$:

$$a+bi = 4 + 12i + 9(-1)$$ $$a+bi = 4 + 12i - 9$$ $$a+bi = (4-9) + 12i$$ $$a+bi = -5 + 12i$$

For two complex numbers to be equal, their real parts must be equal and their imaginary parts must be equal.
Comparing the real parts:

$$a = -5$$

Comparing the imaginary parts:

$$b = 12$$

The values are:

$$a = -5, b = 12$$