SOLUTION: Multiply: (1/6 – i)^2

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Question 195737: Multiply: (1/6 – i)^2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28z-i%29%5E2 Start with the given expression.


%281%2F6-i%29%281%2F6-i%29 Expand. Remember something like x%5E2=x%2Ax.


Now let's FOIL the expression.


Remember, when you FOIL an expression, you follow this procedure:


%28highlight%281%2F6%29-i%29%28highlight%281%2F6%29-i%29 Multiply the First terms:%281%2F6%29%2A%281%2F6%29=%281%2F6%29%5E2=1%2F36.


%28highlight%281%2F6%29-i%29%28z%2Bhighlight%28-i%29%29 Multiply the Outer terms:%281%2F6%29%2A%28-i%29=-%281%2F6%29%2Ai.


%281%2F6%2Bhighlight%28-i%29%29%28highlight%281%2F6%29-i%29 Multiply the Inner terms:%28-i%29%2A%281%2F6%29=-%281%2F6%29%2Ai.


%281%2F6%2Bhighlight%28-i%29%29%281%2F6%2Bhighlight%28-i%29%29 Multiply the Last terms:%28-i%29%2A%28-i%29=i%5E2=-1.


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So we have the terms: 1%2F36, -%281%2F6%29%2Ai, -%281%2F6%29%2Ai, and -1


1%2F36-%281%2F6%29%2Ai-%281%2F6%29%2Ai-1 Now add every term listed above to make a single expression.


-35%2F36-%281%2F3%29i Now combine like terms.


So %281%2F6-i%29%5E2 FOILs to -35%2F36-%281%2F3%29i.


In other words, %281%2F6-i%29%5E2=-35%2F36-%281%2F3%29i.