70.0k views
5 votes
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

Rationalize the denominator of square root of negative 49 over open parentheses 7 minus-example-1

2 Answers

0 votes

Answer:

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

User Pazonec
by
7.7k points
1 vote

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.

User JfMR
by
8.4k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.