Question

Simplify the expression to a + bi form:(12 – 6i)(3 – 10i)

Answer 1

Given the expression:

`(12-6i)(3-10i)`

To simplify in the form:

`a+bi`

step 1:

Multiply the terms in the second parenthesis by each term in the first parenthesis.

Thus,

`\begin{gathered} 12(3-10i)-6i(3-10i) \\ \Rightarrow36-120i-18i+60i^2 \end{gathered}`

step 2:

Collect like terms.

`\begin{gathered} 36-120i-18i+60i^2 \\ \text{but } \\ i^2=-1 \\ \text{thus,} \\ 36+60(-1)-120i-18i \\ \Rightarrow36-60-120i-18i \\ =-24-138i \\ \Rightarrow-24+(-138)i \end{gathered}`

Hence, the expression is simplified as

`-24+(-138)i`