3 years ago

The hypotenuse of a right triangle measures 2 sqrt 15 centimeters and its shorter leg measures 2 sqrt 6

Mathematics

1 answer:

ioda3 years ago

3 0

Answer: please see the attachments for the solution.

Step-by-step explanation:

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Simplify the expression fraction with numerator of the square root of negative four and denominator of the quantity three plus i

Alex787 [66]

Answer:

$\frac{-4+2i}{5}$

Step-by-step explanation:

We are given the expression, $\frac{\sqrt{-4}}{(3+i)-(2+3i)}$

On simplifying, we have,

$\frac{2i}{3+i-2-3i}$

i.e. $\frac{2i}{1-2i}$

Now, we will rationalize the expression,

i.e. $\frac{2i}{1-2i}\times \frac{1+2i}{1+2i}$

i.e. $\frac{(2i)\times (1+2i)}{(1-2i)\times (1+2i)}$

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i.e. $\frac{2i-4}{1+4}$

i.e. $\frac{-4+2i}{5}$

So, the simplified expression is $\frac{-4+2i}{5}$ .

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