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

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

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Answer 1 · 2015-11-29T13:27:32

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

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