SOLUTION: Can I have some help with this expression? Evaluate the expression and write the result in the form a + bi. 1/(9 + 2i) - 1/(2 + i)

Algebra ->  Equations -> SOLUTION: Can I have some help with this expression? Evaluate the expression and write the result in the form a + bi. 1/(9 + 2i) - 1/(2 + i)      Log On


   

Question 120688: Can I have some help with this expression?
Evaluate the expression and write the result in the form a + bi.
1/(9 + 2i) - 1/(2 + i)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
In order to simplify this, we need to get everything into standard form.

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Start with the first part of the expression.

Multiply the fraction by

Foil and Multiply


Break up the fraction. So it is now in a%2Bbi form where a=9%2F85 and b=-2%2F85

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Start with the second part of the expression

Multiply the fraction by

Foil and Multiply


Break up the fraction. So it is now in a%2Bbi form where a=2%2F5 and b=-1%2F5



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So we the expression goes from and becomes:





Distribute the negative


Group like terms


Combine like terms



So simplifies to



In other words