I have a Alg.II question concerning imaginary numbers.?

Well, start off with this:

√-7 = √(7x-1) = √7 x √(-1) = √7 x i

Leaving:

√56/i√7 Multiply top and bottom by i, remembering that i x i = -1

i√56/-√7 Multiply top and bottom by √7 (and remember negative on the bottom makes the whole thing negative)

-i√56x√7/7 Multiply the square roots

-i√392/7

That is the exact answer. If you want a decimal approximation, punch in √392/7 into your calculator to get 2.828427, combine with -i to get:

-i2.828427

The answer is - square root of 2....

you may or you may not simplify the numerator first but it will be easier if you do so.

simplifying the numerator will give, 2 square root of 14 / square root of -7...

then rationalize the denominator which will give you 2 square root of -98 / 7i

then simplify, -7i square root of 2/ 7i will give you -square root of 2

You multiply appropriate and backside by using the complicated conjugate of the denominator. in this occasion it relatively is (4i - 2): (3 - 7i)(4i - 2)/(4i + 2)(4i - 2) = [3(4i - 2) - 7i(4i - 2)] / [4i(4i - 2) + 2(4i - 2)] = [12i - 6 - 28i^2 + 14i] / 16i^a million - 8i + 8i - 4 = (26i - 6 + 28) / (-sixteen - 4) because of the fact that i^2 = -a million = (26i + 22) / -20 = 22/20 - 26i/20 = 11/10 - i *13/10 this is interior the conventional way of providing a complicated huge form. notice that the i could nicely be placed after the 13/10.