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

1 Answer
Nov 29, 2015

Answer:

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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