Working Late

[Marvin08]

Hi you guys im back for the last time this week with some questions. I had to work tonight and wasn't able to get around to this extra credit my trig teacher gave me. I did some of it but here are some that challenged me.
Simplify
Radical -6*radical -12

Simplify

(9+7i) + ( 15+8i)

Simplify

2+i Note: This problem is supposed to be directly over each other
3- i

Solve
3x squared + 15 =0

The rest of them i seem to be fine on i just needed help with these because our chapter quiz is quickly approaching. Thanks for all the help i really appreciate it.

 

[Denis]

Solve
3x squared + 15 =0

3x^2 + 15 = 0 : are you saying you can't do this one?

Do you know what "i" stands for?

 

[Marvin08]

im saying he told me my answer was wrong, and no im not sure what i satnds for but i know its not just like a regular variable.

 

[jonboy]

Hi Marvin!

On the first we have: \(\displaystyle \L \;\sqrt{\,-\,6}\,\cdot\,\sqrt{\,-\,12}\)

This can be rewritten as: \(\displaystyle \L \;\sqrt{6}\,\cdot\,\sqrt{\,-\,1}\cdot\,\sqrt{12}\,\cdot\,\sqrt{\,-\,1}\)

\(\displaystyle i\) is an imaginary number and is \(\displaystyle \sqrt{\,-\,1}\)

So let's sub \(\displaystyle i\) for \(\displaystyle \sqrt{\,-\,1}\): \(\displaystyle \L \;\sqrt{6}i\,\cdot\,\sqrt{12}i\)

Multiply like terms: \(\displaystyle \sqrt{72}i^2\,=\,\sqrt{2^3\,\cdot\,3^2}i^2\,=\,6\sqrt{2}i^2\)

So what does \(\displaystyle i^2\) equal?

\(\displaystyle (i)^2\,=\,(\sqrt{\,-\,1})^2\,\;\;\Rightarrow\;\;{\,i^2\,=\,-\,1}\)

Sub that in for \(\displaystyle i^2\): \(\displaystyle \L \;6\sqrt{2}(-\,1)\,=\,-6\sqrt{2}\)

 

[jonboy]

On the second just add like terms as if you had:

\(\displaystyle 9\,+\,7x\,+\,15\,+\,8x\)

Now you just have a \(\displaystyle i\) instead \(\displaystyle x\)

For the third look up conjugates.

 

[stapel]

he told me my answer was wrong

We'll be glad to check your work, but you'll need to post it. Thank you!

no im not sure what i satnds for...

Ah. So you missed a week or so of lessons, and a chapter in the book. Ouch! :shock:

Fortunately, there are loads of lessons available online. Please study a few of them, until you feel you have a good grasp of what the "imaginary" "i" is, and how complex numbers work, especially in the context of the Quadratic Formula.

Once you have that background, the tutors' hints, etc, will make a lot more sense! :wink:

Eliz.