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Nesterboy [21]
3 years ago
10

Simplify the given expression below 4/3-2i

Mathematics
2 answers:
ANTONII [103]3 years ago
4 0
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)}\\\\
-------------------------------\\\\
recall\qquad i^2=-1\\\\
-------------------------------\\\\
\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
sergejj [24]3 years ago
4 0
Multiply by the conjugate (flip the symbol in the denominator and multiply numerator and denominator by it): 
\frac{4\left(3+2i\right)}{\left(3-2i\right)\left(3+2i\right)}

Distribute on top and bottom; for bottom: 
3^2+\left(-2\right)^2=13

For top: 
4\cdot \:3+4\cdot \:2i=12+8i

Now we have:
\frac{12+8i}{13}

Final answer: 
\frac{12}{13}+\frac{8}{13}i

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Answer:

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Step-by-step explanation:

You can save yourself some trouble if you realize that one of the angles in one pair must match one of the angles in the other pair.

This observation eliminates the first two choices.

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Going further, the triangles will be similar if the dissimilar angles together with one of the similar angles totals 180°.

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Triangle 1 – ∠1 = 50°, ∠2 = 30°

Triangle 2 – ∠2 = 20°, ∠3 = 100°  . . . . . no angles match

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Triangle 1 – ∠1 = 60°, ∠2 = 20°

Triangle 2 – ∠1 = 40°, ∠3 = 100°  . . . . . no angles match

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Triangle 1 – ∠1 = 25°, ∠2 = 115°

Triangle 2 – ∠1 = 25°, ∠3 = 40° . . . . 25° angles match; 25+40+115 = 180

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Triangle 2 – ∠2 = 15°, ∠3 = 160° . . . . 15° angles match; 15+5+160 = 180

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7 0
2 years ago
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Answer:

54m2

Step-by-step explanation:

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Taking area of first one=24m2,then area of the second =30m2.

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Step-by-step explanation:

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