Question

Rationalize the denominator of square root of negative 36 over open parentheses 2 minus 3 i close parentheses plus open parentheses 3 plus 2 i

Answer 1

start by simplifying the denominator expression:

(2 - 3i) + (3 + 2i) = 2 + 3 - 3i + 2i
= 5 - i

Does that make sense so far?

Answer 2

yes

Answer 3

square root of -36 gives 6i on the top.

But to rationalize the bottom, you have to multiply by the complex conjugate... so since we found (5 - i) on the bottom, you multiply top and bottom by (5 + i).

Then, there's a bunch of simplifying at the end.

Answer 4

ok

Answer 5

simplifying that last expression...
= -6/26 + 30i/26
= -3/13 + (15/13)i

Looks weird, but that's what I got. Without seeing your work, I'm not sure where we did it differently.

Answer 6

thats fine with me

Answer 7

At the end, though, you want the answer in the form of a number plus or minus some quantity with "i"... that is the form A + Bi, where A is the real number part and Bi is the imaginary part.

Answer 8

soooo... i hope I helped

Answer 9

thanks

Answer 10

np