SOLUTION: What does the product (4+7i)(2-5i) equal? What does the quotient (1+4i)/(5-2i) equal?

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Question 173218: What does the product (4+7i)(2-5i) equal?

What does the quotient (1+4i)/(5-2i) equal?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1

%284%2B7i%29%2A%282-5i%29 Start with the given expression.


%284%29%282%29%2B%284%29%28-5i%29%2B%287i%29%282%29%2B%287i%29%28-5i%29 FOIL.


8-20i%2B14i-35i%5E2 Multiply.


8-20i%2B14i-35%28-1%29 Replace i%5E2 with -1. Note: i%5E2=-1.


8-20i%2B14i%2B35 Multiply.


43-6i Combine like terms.


So %284%2B7i%29%2A%282-5i%29=43-6i.


So the expression is now in standard form a%2Bbi where a=43 and b=-6







# 2


%281%2B4i%29%2F%285-2i%29 Start with the given expression.


%28%281%2B4i%29%2F%285-2i%29%29%28%285%2B2i%29%2F%285%2B2i%29%29 Multiply the fraction by %285%2B2i%29%2F%285%2B2i%29 (which is the complex conjugate of the denominator).


%28%281%2B4i%29%285%2B2i%29%29%2F%28%285-2i%29%285%2B2i%29%29 Combine the fractions.


FOIL the numerator.


FOIL the denominator.


%285%2B2i%2B20i%2B8i%5E2%29%2F%2825%2B10i-10i-4i%5E2%29 Multiply.


%28-3%2B22i%29%2F%2829%29 Combine like terms.


-3%2F29%2B%2822%2F29%29%2Ai Break up the fraction.


So %281%2B4i%29%2F%285-2i%29=-3%2F29%2B%2822%2F29%29%2Ai.


So the expression is now in standard form a%2Bbi where a=-3%2F29 and b=22%2F29