Checking my math work

[EunSoo]

Hello! So here is a problem I am trying to simplify for my math class but it really doesn't look right. Could someone here make sure I did it right and that my answer is right? I feel like I congugated twice and did extra steps that might have changed the answer. The problem is the first part in parenthesis and then the arrows symbolize going to each step and my answer is boxed:

 

Thanks for the help!

[orbitalbuzzsaw]

Looks OK, but I didn't check too carefully. There's probably a website that'll check it for you.

[EunSoo]

2 minutes ago, orbitalbuzzsaw said:

Looks OK, but I didn't check too carefully. There's probably a website that'll check it for you.

good call. I checked it out on Mathway and it came up with this:

So I must have done somehting wrong. I think that somewhere I should have gotten an i^2 that I could have turned into a -1.

 

[orbitalbuzzsaw]

Just now, SCGazelle said:

good call. I checked it out on Mathway and it came up with this:

So I must have done somehting wrong. I think that somewhere I should have gotten an i^2 that I could have turned into a -1.

 

Yeah. I knew all this imaginary number stuff once. Key word : once.

[NannerBeans]

The last part in the top row is wrong, you can't cancel like that. 

[NannerBeans]

Also, the first part of the 2nd line, you can't add 1/1, you can only multiple by 1/1. 

 

Edit: You can't cancel like the way you did at that step either. 

[TheKDub]

31 minutes ago, SCGazelle said:

Hello! So here is a problem I am trying to simplify for my math class but it really doesn't look right. Could someone here make sure I did it right and that my answer is right? I feel like I congugated twice and did extra steps that might have changed the answer. The problem is the first part in parenthesis and then the arrows symbolize going to each step and my answer is boxed:

 

Thanks for the help!

 

First step is wrong, you multiply it by it's conjugate, not by itself.
So 

( sqrt(3) + 2i )     ( sqrt(3) + 2i )

( sqrt(3) - 2i )   *  ( sqrt(3) + 2i )

The answer is...

 

-1 + 4i sqrt(3)
          7

 

or

-1  +   4i sqrt(3)

7              7

[NannerBeans]

1 minute ago, TheKDub said:

 

First step is wrong, you multiply it by it's conjugate, not by itself.
So 

( ( sqrt(3) + 2i ) / ( sqrt(3) - 2i ) ) * ( ( sqrt(3) + 2i ) / ( sqrt(3) + 2i ) )

The answer is...

Yeah I was going to mention this but I was too lazy to write out the equation lol. 

[Dash Lambda]

- You want to use the conjugate of the denominator.

- When multiplying out in the first line, you forgot to square i: (sqrt(3) + 2i)(sqrt(3) - 2i) = 3 + sqrt(3)2i - sqrt(3)2i + 4

- You cannot cancel terms through addition/subtraction, only multiplication/division.

- You cannot cancel denominators when adding fractions.

- Adding 1 changes the value.

[EunSoo]

13 minutes ago, Dash Lambda said:

- You want to use the conjugate of the denominator.

- When multiplying out in the first line, you forgot to square i: (sqrt(3) + 2i)(sqrt(3) - 2i) = 3 + sqrt(3)2i - sqrt(3)2i + 4

- You cannot cancel terms through addition/subtraction, only multiplication/division.

- You cannot cancel denominators when adding fractions.

- Adding 1 changes the value.

 

22 minutes ago, NannerBeans said:

Yeah I was going to mention this but I was too lazy to write out the equation lol. 

 

24 minutes ago, TheKDub said:

 

First step is wrong, you multiply it by it's conjugate, not by itself.
So 

( ( sqrt(3) + 2i ) / ( sqrt(3) - 2i ) ) * ( ( sqrt(3) + 2i ) / ( sqrt(3) + 2i ) )

The answer is...

 

26 minutes ago, NannerBeans said:

Also, the first part of the 2nd line, you can't add 1/1, you can only multiple by 1/1. 

 

Edit: You can't cancel like the way you did at that step either. 

 

31 minutes ago, NannerBeans said:

The last part in the top row is wrong, you can't cancel like that. 

Wow. I can't believe I made most of those mistakes and couldn't catch them myself lol. Though I didn't know that I should be using the congugate of the dominator but now that I think about it, it makes sense. Maybe I should take a break before I do my next problem. Anyways, here is my work, does it look right?

[79wjd]

3 minutes ago, SCGazelle said:

 

Anyways, here is my work, does it look right?

 

yep

[apple010]

Just made it to the bottom of your "Reveal hidden contents" thing. Leaving it there  

[TheKDub]

5 minutes ago, SCGazelle said:

 

Spoiler

 

Looks right to me.

 

Just a tip, when multiplying conjugates using the FOIL method, you can skip multiplying the outside and the inside as they'll just cancel out. (Still multiply the firsts and the lasts.)

As an example, (5x+2)(5x-2) -> 25x + 10x - 10x - 4 = 25x - 4

You'd just multiply the 5x and 5x, then the 2 and -2, skipping over multiplying 5x and -2, and 5x and 2.

[themctipers]

just pretending to know what is going on!  shit , math going to be hell ... 

[EunSoo]

@NannerBeans @TheKDub @Dash Lambda thanks a ton for your help. It's a good thing I got this figured out as this is the first of many problems like it.

[TheKDub]

Just now, SCGazelle said:

@NannerBeans @TheKDub @Dash Lambda thanks a ton for your help. It's a good thing I got this figured out as this is the first of many problems like it.

Feel free to ask if you need any more help. But don't turn us into a crutch.