namely, let's rationalize the denominator in the fraction, for which case we'll be using the conjugate of that denominator, so we'll multiply top and bottom by its conjugate.

so the denominator is 5 + i, simply enough, its conjugate is just 5 - i, recall that same/same = 1, thus (5-i)/(5-i) = 1, and any expression multiplied by 1 is just itself, so we're not really changing the fraction per se.

$\bf \cfrac{2}{5+i}\cdot \cfrac{5-i}{5-i}\implies \cfrac{2(5-i)}{\stackrel{\textit{difference of squares}}{(5+i)(5-i)}}\implies \cfrac{2(5-i)}{\stackrel{\textit{recall }i^2=-1}{5^2-i^2}}\implies \cfrac{2(5-i)}{25-(-1)} \\\\\\ \cfrac{2(5-i)}{25+1}\implies \cfrac{2(5-i)}{26}\implies \cfrac{5-i}{13}$

4 0

3 years ago

What is 37% of 293? Plz help me people this is for tomorrow

stira [4]

108.41 i pretty sure

5 0

3 years ago

Read 2 more answers

Parametrizations help needed

erica [24]

Sorry I don't know that either

6 0

4 years ago

Ted is saving for a toy. He has no money now, but

sweet-ann [11.9K]

Answer:

4D - 1

Step-by-step explanation:

So, if Ted saves $D for 4 weeks, then this amount will be equal to 4D because multiplication is simply repeated addition. We can imagine this situation as D+D+D+D, for the 4 weeks he is saving. We can simplify this to 4D in the expression.

Next, the question tells us that this will be 1 dollar more than needed. So, if we want to find the cost, we need to subtract that dollar.

Thus, the final expression is 4D - 1 because this represents 1 dollar less than the money he saves for 4 weeks.

6 0

2 years ago