In step 1 why did you multiple Z by 2-3i/ 2-3i

Multiplying a complex number by its conjugate results in a real number:

$$(a+bi)(a-bi) = a^2 - (bi)^2 = a^2 - b^2i^2 = a^2 + b^2$$

In Step 1, the denominator was $2+3i$. Its conjugate is $2-3i$.
Multiplying the denominator by $2-3i$ makes it a real number:

$$(2+3i)(2-3i) = 2^2 + 3^2 = 4+9 = 13$$

To maintain the value of the fraction, the numerator must also be multiplied by the same term, $2-3i$. This is equivalent to multiplying the entire fraction by $\frac{2-3i}{2-3i}$, which is equal to 1.