Question

Rationalize the denominator of square root of negative 49 over (7 - 2i) - (4 + 9i)

Answer 1

the choices are
\[\frac{ −49+2i }{−40 }\]

\[\frac{ 49+21i }{ 58 }\]

\[\frac{ 77+21i}{ -2 }\]

\[\frac{ −77+21i }{ 130 }\]

Answer 2

The problem looks like \[\frac{ \sqrt{-49} }{ (7 - 2i) - (4 + 9i) }\]

Answer 3

ok... so in the numerator use i^2 = -1

and also simplify the denominator by collecting like terms

\[\frac{\sqrt{49i^2}}{3 - 11i}\]

now multiply by the conjugate pair

\[\frac{7i}{3 - 11i} \times \frac{3 + 11i}{3 + 11i}\]

do the multiplication and then simplify

Answer 4

How do I multiply them? Like straight across or

Answer 5

The answer is

\[\frac{ -77+21i }{ 130}\]

Answer 6

I showed the way to solve in the other question

Answer 7

why give an answer.... how does that help understanding... ?

and yes you multiply straight across, just like multiplying any 2 fractions

\[\frac{7i(3 + 11i)}{(3 - 11i)(3 + 11i)}\]

you should recognise the denominator is the difference of 2 squares...

hope it helps