Question

Please, tell me what to do without giving me the answer.

Perform the indicated operations and leave your answer in simplest form. Assume all variables are unrestricted except by natural domains.

1) l 3 - 4i l

2) cube root of (1/9 (x-5)^2 + 5)

Answer 1

#2 looks like this

\[\sqrt[3]{\frac{ 1 }{ 9 }(x -5)^{2}+5}\]

Answer 2

The first one is finding the abs value or magnitude of the imaginary number
The second one, you're going to use DeMoivre's formula to solve the equation

Ready?

Answer 3

So, for the first one, I have to find the distance of the real and imaginary part of it? Would the real part be 3 and the imaginary part 4i?

And for the second one, what is DeMoivre's formula? We never went over that in class so its new to me.

Answer 4

Sorry, I used the wrong method for the second one, we'll get back to that.

Answer 5

For the first one, to find the magnitude of a complex number (a number made up of an imaginary and a real part
real: has no i on it
imaginary: has an i on it

where i=\[\Large \sqrt{-1}\])

Answer 6

The formula is this where a and b are real number and bi is the imaginary part however\[ \Large \left| a+bi \right|=\sqrt{a^2+b^2}\]

Answer 7

So you got to plug in the numbers for a and b and solve

Answer 8

oh, so i would have a=3 and b=4 which makes that \[\sqrt{(3)^{2}+(4)^{2}}\] and my answer would be 25. Is that correct?

Answer 9

sqrt it

Answer 10

Oh, sorry. So my final answer is 5. Thank you! However, for the second one, will I multiply everything first?

Answer 11

I'm trying to find out the method for doing this, I would suppose that you don't multiply it out

Answer 12

I'm just gonna go with it in simplified form

Answer 13

First you gotta expand the (x-5)^2

Answer 14

like (x-5)(x-5) or (x^2 - 10x +25) ?

Answer 15

Correct. Now I would say to multiply the whole expression you multiplied through by 1/9 but it'll be eaiser to just put everything over 9 just\[\Large \frac{ x^2-10x+25 }{ 9 }+5\] like this

Answer 16

And then you would convert that 5 at the end into a number of 9 so that we can add it to the whole expression. What number would that be?

Answer 17

45/9? and that makes it \[\frac{ x ^{2}-10x+25+45 }{ 9 }\] do i simplify it afterwards and then cube root it? Or am I missing a step?

Answer 18

Yeah and then combine to get 70 as the constant

Answer 19

And all of that will have to get 1/9 factored out (I only multiplied it to combine it with the 5 and then take it out) and you end up with \[\Large \sqrt[3]{\frac{1}{9} (x ^{2}-10x+70)}\]

Answer 20

You gotta separate the 1/9 ftom the rest of the expression \[\sqrt[3]{a \times b}=\sqrt[3]{a}\times \sqrt[3]{b}\]

Answer 21

\[\Large \sqrt[3]{\frac{1}{9}}\times \sqrt[3]{(x ^{2}-10x+70)}\]

Answer 22

The Right Hand Side can be simplified to \[\Large (x ^{2}-10x+70)^\frac{1}{3}\]

Answer 23

do i do the same thing for the left hand side?

Answer 24

The cbrt(1/9) can be rationalized to \[\Large \sqrt[3]{\frac{ 1 }{ 9 }}=\frac{ 1}{ \sqrt[3]{9} } \times \frac{ \sqrt[3]{9} }{ \sqrt[3]{9} } \times \frac{ \sqrt[3]{9} }{ \sqrt[3]{9}}\]

Answer 25

\[\Large \frac{ \sqrt[3]{81} }{ 9 }\]

Answer 26

\[\Large \frac{ \sqrt[3]{81} }{ 9 } \times (x ^{2}-10x+70)^\frac{1}{3}\] would be your final answer, I don't know if they want it simplified more but that's it, I gotta go, good luck!!1

Answer 27

thank you! :D