How Do You Simplify Conjugate Expressions?

[aisha]

1) (-7+20)(-10-3i)

2) (-2-5i)/(3+4i)

I don't think I did these two questions right does anyone know how?

 

[arildno]

Multiply with 1, written in terms of the conjugate expressions of the denominators.

 

[aisha]

I simplified (-7+2i)(-10-3i) and got 76+i is this correct?

 

[cdhotfire]

yes, that is correct.

 

[HawKMX2004]

1) (-7+20)(-10-3i)

Step 1.) FOIL the Problem
Step 2.) Simplify from there (Do addition Subtraction etc.)

2) (-2-5i)/(3+4i)

I forgot how to do division with imaginary numbers I'll try to look it back up and give you some help

 

[kreil]

All you need to know to solve these sort of problems is that:
$$i=\sqrt{-1}$$
$$i^2 = -1$$
$$i^3 = -i$$
$$i^4 = 1$$ and the cycle repeats

so to take your question:
$$(-7+2i)(-10-3i)$$
$$70+21i-20i-6i^2$$
$$76+i$$

you did in fact do it correctly.

 

[cdhotfire]

hey, for that latex all i have 2 do is put [-code-] the code and end. Correct?
let me try.
seems i have 2 put latex
$$\theta$$

 

[aisha]

1) (-7+20)(-10-3i)

Step 1.) FOIL the Problem
Step 2.) Simplify from there (Do addition Subtraction etc.)

2) (-2-5i)/(3+4i)

I forgot how to do division with imaginary numbers I'll try to look it back up and give you some help

Thanks for taking the time to look it up, and thanks everyone who told me the first one is right what a relief! For simplifying (-2-5i) / by (3+4i) I got (-26-7i)/25 as my final answer can someone tell me is this right?

 

[vladimir69]

yes you are right again
(-2-5i)/(3+4i) does equal (-26-7i)/25

 

[aisha]

Yay!

yes you are right again
(-2-5i)/(3+4i) does equal (-26-7i)/25

Thanks sooo much! If anyone has any objections they may still speak