SOLUTION: multiply. write result in the form a+bi (6+5i)^2

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Question 599389: multiply. write result in the form a+bi
(6+5i)^2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%286%2B5i%29%5E2 Start with the given expression.


%286%2B5i%29%286%2B5i%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%286%29%2B5i%29%28highlight%286%29%2B5i%29 Multiply the First terms:%286%29%2A%286%29=36.


%28highlight%286%29%2B5i%29%286%2Bhighlight%285i%29%29 Multiply the Outer terms:%286%29%2A%285%2Ai%29=30%2Ai.


%286%2Bhighlight%285i%29%29%28highlight%286%29%2B5i%29 Multiply the Inner terms:%285%2Ai%29%2A%286%29=30%2Ai.


%286%2Bhighlight%285i%29%29%286%2Bhighlight%285i%29%29 Multiply the Last terms:%285i%29%2A%285i%29+=+25i%5E2=25%28-1%29=-25.


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So we have the terms: 36, 30%2Ai, 30%2Ai, -25


36%2B30%2Ai%2B30%2Ai-25 Now add every term listed above to make a single expression.


11%2B60i Now combine like terms.


So %286%2B5i%29%5E2 FOILs to 11%2B60i.


In other words, %286%2B5i%29%5E2=11%2B60i.