3. Let $z_{1}=5+6 i, z_{2}=-i-1$ and $z_{3}=4 i$. (a) Write the following in the form $a+i b$ : i. $2 z_{1}-3 z_{2}+z_{3}$

Step 1 ：Let $z_{1}=5+6 i, z_{2}=-i-1$ and $z_{3}=4 i$.

Step 2 ：We need to calculate the expression $2z_1 - 3z_2 + z_3$ and represent it in the form $a + ib$.

Step 3 ：\(2z_1 - 3z_2 + z_3 = 2(5+6i) - 3(-1-i) + 4i\)

Step 4 ：\(= (10+12i) + (3+3i) + 4i\)

Step 5 ：\(= (13+19i)\)

Step 6 ：\(\boxed{13 + 19i}\)