Is the answer for (3 + i) / (6 - i) correct?

[elie_girl]

1. Rationalize the numerator sqrt(5)+3/-4sqrt(7).


(sqrt(5) + 3) / (-4)(sqrt(7)) =
(sqrt(5) + 3)(sqrt(5) - 3) / (-4)(sqrt(7))(sqrt(5) - 3) =
(5 - 9) / (-4)(sqrt(7))(sqrt(5) - 3) =
-4 / (-4)(sqrt(7))(sqrt(5) - 3) =
1 / (sqrt(7))(sqrt(5) - 3)

2. Perform the operation. Write the answer in a + bi form. 3+i/6-i I do this problem and I get the answer (17+9i)/37 is that right?

(3 + i) / (6 - i) =
(3 + i)(6 + i) / (6 - i)(6 + i) =
18 + 9i -1 / 36 + 1
17 + 9i / 37

 

[LowlyPion]

1. Rationalize the numerator sqrt(5)+3/-4sqrt(7).


(sqrt(5) + 3) / (-4)(sqrt(7)) =
(sqrt(5) + 3)(sqrt(5) - 3) / (-4)(sqrt(7))(sqrt(5) - 3) =
(5 - 9) / (-4)(sqrt(7))(sqrt(5) - 3) =
-4 / (-4)(sqrt(7))(sqrt(5) - 3) =
1 / (sqrt(7))(sqrt(5) - 3)

2. Perform the operation. Write the answer in a + bi form. 3+i/6-i I do this problem and I get the answer (17+9i)/37 is that right?

(3 + i) / (6 - i) =
(3 + i)(6 + i) / (6 - i)(6 + i) =
18 + 9i -1 / 36 + 1
17 + 9i / 37

Looks OK to me.

 

[elie_girl]

Well I keep submitting then into my homework and I still get them wrong. I don't know what else to do.

 

[LowlyPion]

Your denominator in 1) should probably combine the √5*√7 as √35

 

[LowlyPion]

In 2) it asks for the answer in the form C = a + b*i

Hence = 17/37 + (9/37)*i

 

[elie_girl]

oh ok thanks! It worked.