Question

How do you multiply imaginary numbers of the form a + bi?

Answer 1

See explanation

Explanation:

`color(blue)("Comment")`

Example
`("Real part" + "Imaginary part") ->(Re+Im)-> (6+12i)`
Notice that I keep the brackets. This is important as the 'Real' part,6, contributes to the whole. As does the Imaginary part of 12i. So together they are the whole of something.

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The distributive law applies

`color(blue)("Case 1")color(white)(....) cxx(a+bi)`

Write as : `(cxxa)+(cxxb)i-> (ca+cbi)`

Using the actual numbers previously chosen at random:

`3(2+6i)-> (6+12i)`

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`color(blue)("Case 2")color(white)(....) (a+bi)(c+di)`

This would be easier to demonstrate with numbers

Suppose we had: `(2+i)(3+4i)`

`2(3+4i) +i(3+4i)`

`6+8i+3i+4i^2`

`6+11i+4i^2`

But `i=sqrt(-1)" so " i^2=(-1)`

`6+11i+4(-1)`

`2+11i`
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