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

The answer is the option d, which is: d) $\frac{-77+21i}{130}$

The explanation for this problem is shown below:

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

$\frac{7i}{7-2i-4-9i} \\\frac{7i}{3-11i}$

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

$\frac{7i(3+11i)}{(3-11i)(3+11i)} \\ \frac{21i+77i^{2}}{121+9} \\ \frac{-77+21i}{130}$

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