Question

Simplify the expression the root of negative four all over the quantity of five plus two i minus the quantity of three minus four i.

Answer 1

\[\frac{\sqrt{-4}}{(5+2i)-(3-4i)}\]

Answer 2

@campbell_st think you can help?

Answer 3

well you can simplify the denominator as \[5 +2i - 3 + 4i = 2 + 7i\]

the numerator is

\[\sqrt{-4} = \sqrt{4i^2} = \pm 2i\]

you probably only need to use 2i

so the problem is now

\[\frac{2i}{2 + 7i}\]

you'll probably need to rationalise the denominator... to get the final solution.

hope it helps

Answer 4

7i? i thought it was 6i .@campbell_st

Answer 5

the answers they give are
3+i/10
3-i/10
3+1/8
3-i/8
@campbell_st

Answer 6

@ganeshie8 think you can help?

Answer 7

@Hero @whpalmer4 how about yall?

Answer 8

oops yes it is 6i...

so to rationalise the denominator use the idea of the difference of 2 squares

\[\frac{2i}{2 + 6i} \times \frac{2 - 6i}{2-6i}\]

which becomes

\[\frac{2i(2 - 6i)}{4 + 36}\]

can you finish it from here...?

Answer 9

\[\frac{ 4i-12i^2 }{ 40 }\]

Answer 10

@campbell_st

Answer 11

well remember \[i^2 = -1\]

so its

\[\frac{4i + 12}{40}\]

remove the commone factor of 4 for the answer