Question

Rationalize the denominator of square root of negative 49 over open parentheses 7 minus 2 i close parentheses minus open parentheses 4 plus 9 i.

a) -49+2i/-40
b)49+21i/58
c)77+21i/-2
d)-77+21i/130

Answer 1

Explanation:

Rationalize the denominator of square root of negative 49 over open parentheses 7 minus 2 i close parentheses minus open parentheses 4 plus 9 i.

a) -49+2i/-40

b)49+21i/58

c)77+21i/-2

d)-77+21i/130

Answer 2

The answer is the option d, which is: d)
`(-77+21i)/(130)`

The explanation for this problem is shown below:

1. Smplify the denominator and rewrite the numerator in this form:

`(7i)/(7-2i-4-9i) \\(7i)/(3-11i)`

2. Multiply the denominator and the numerator by the conjugated
`(3+11i)` and simplify the expression, as following:

`(7i(3+11i))/((3-11i)(3+11i)) \\ (21i+77i^(2))/(121+9) \\ (-77+21i)/(130)`

3. As you can see, you obtain the expression shown in the option mentioned above.