Question

Express the following expression in the form of a + bi: (9 + 14i) ((6 – 5i) + (3 - 4i)).

Answer 1

Remember the following rules for multiplying and adding complex numbers:

`\begin{gathered} (a+bi)+(c+di)=(a+c)+(b+d)i \\ \\ (a+bi)(c+di)=(ac-bd)+(ad+bc)i \end{gathered}`

First, solve the expression inside the parenthesis:

`(6-5i)+(3-4i)=(6+3)+(-5-4)i=9-9i`

Next, multiply the two remaining complex numbers:

`\begin{gathered} (9+14i)((6-5i)+(3-4i))=(9+14i)(9-9i) \\ \\ =(9\cdot9-14\cdot-9)+(9\cdot-9+14\cdot9)i \\ \\ =(81+126)+(-81+126)i \\ \\ =207+45i \end{gathered}`

Therefore, the answer is: 207 + 45i.