SOLUTION: Write in standard form: (3-2i)^2

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Question 148307: Write in standard form: (3-2i)^2
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!

%283-2i%29%5E2 Start with the given expression.


%283-2i%29%283-2i%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%283%29-2i%29%28highlight%283%29-2i%29 Multiply the First terms:%283%29%2A%283%29=9.


%28highlight%283%29-2i%29%283%2Bhighlight%28-2i%29%29 Multiply the Outer terms:%283%29%2A%28-2%2Ai%29=-6%2Ai.


%283%2Bhighlight%28-2i%29%29%28highlight%283%29-2i%29 Multiply the Inner terms:%28-2%2Ai%29%2A%283%29=-6%2Ai.


%283%2Bhighlight%28-2i%29%29%283%2Bhighlight%28-2i%29%29 Multiply the Last terms:%28-2%2Ai%29%2A%28-2%2Ai%29=4%2Ai%5E2=4%28-1%29=-4.


9-6%2Ai-6%2Ai-4 Now collect every term to make a single expression.


5-12%2Ai Now combine like terms.


Now the number is in standard form a+bi where a=5 and b=-12