Question

What is the product of (-2+ 3i) and (4 – 5i) in a + bi torm?Part B:Fxplain how you determined your answer.

Answer 1

Given complex numbers are,

`(-2+3i),(4-5i)`

To find the product of the given complex numbers,

`\begin{gathered} (-2i+3i)(4-5i)=-2i*4+(-2i)(-5i)+3i*4+3i(-5i) \\ \text{ =}-8i+10i^2+12i-15i^2 \end{gathered}`

Now subsitute the value of ,

`i^2=-1`

So we get,

`\begin{gathered} -8i+10i^2+12i-15i^2=-8i+10(-1)+12i-15(-1) \\ \text{ =-8i-10+12i+15} \end{gathered}`

Now add the like terms,

`-8i+12i+15-10=4i+5`

So the required value is in the form,

`a+ib=4i+5`