So-called simplifying, really means, "rationalizing the denominator", which is another way of saying, "getting rid of that pesky radical in the bottom"

$\bf \cfrac{4}{3-2i}\cdot \cfrac{3+2i}{3+2i}\impliedby \textit{multiplying by the conjugate of the bottom}
\\\\\\
\cfrac{4(3+2i)}{(3-2i)(3+2i)}\implies \cfrac{4(3+2i)}{3^2-(2i)^2}\implies \cfrac{4(3+2i)}{3^2-(4i^2)}\\\\
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recall\qquad i^2=-1\\\\
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\cfrac{4(3+2i)}{3^2-(4\cdot -1)}\implies \cfrac{4(3+2i)}{9+4}\implies \cfrac{12+8i}{13}\implies \cfrac{12}{13}+\cfrac{8}{13}i$

4 0

3 years ago

Read 2 more answers

If f(x) = x 2 + 1, find f(a + 1). a 2+ 2 a + 2 a 2 + 2 a 2+ a + 1

goblinko [34]

2a+3

Step-by-step explanation:

5 0

3 years ago

People use water to cook, clean, and drink every day. An estimate of 33.9% of the water used each day is for cooking. If a fam

Lady_Fox [76]

Answer:

23 gallons of water

Step-by-step explanation:

People use water to cook, clean, and drink every day. An estimate of 33.9% of the water used each day is for cooking. If a family uses 67.8 gallons of water a day for cooking, how many gallons do they use every day?

This is calculated as:

33.9 % × 67.8 gallons of water

= 0.339 × 67.8 gallons of water

= 22.9842 gallons of water

Approximately = 23 gallons of water

Therefore, 23 gallons of water are used everyday for cooking

5 0

3 years ago