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3 years ago

How can a conjugate be created from a complex number?

2 answers:

8 0

A conjugate can be created from a complex number The complex conjugate formula is a+bi is a -bi change the signs of the complex number (a-bi is a+bi) the real part is left unchanged.

ratelena [41]3 years ago

5 0

Remember that (a-b)(a+b)=a²-b²
and (imaginary number)²=real

so if we have a+bi, then a-bi is the conguate because (a+bi)(a-bi)=a²+b²

if the complex number is a+bi the conjucate is a-bi

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For Xavier's lemonade recipe, 6 lemons are required to make 4 cups of lemonade. At what rate are lemons being used in cups of le

dusya [7]

Answer:

Since 6 lemons are used to make 4 cups of lemonade, then are used $\frac{6}{4} =\frac{3}{2}$ of lemon per cup of lemonade, or are make $\frac{4}{6}=\frac{2}{3}$ cups of lemonade per lemon.

7 0

3 years ago

The sum of first three terms of a finite geometric series is -7/10 and their product is -1/125. [Hint: Use a/r, a, and ar to rep

Alchen [17]

Ooh, fun

geometric sequences can be represented as
$a_n=a(r)^{n-1}$
so the first 3 terms are
$a_1=a$
$a_2=a(r)$
$a_2=a(r)^2$

the sum is -7/10
$\frac{-7}{10}=a+ar+ar^2$
and their product is -1/125
$\frac{-1}{125}=(a)(ar)(ar^2)=a^3r^3=(ar)^3$

from the 2nd equation we can take the cube root of both sides to get
$\frac{-1}{5}=ar$
note that a=ar/r and ar²=(ar)r
so now rewrite 1st equation as
$\frac{-7}{10}=\frac{ar}{r}+ar+(ar)r$
subsituting -1/5 for ar
$\frac{-7}{10}=\frac{\frac{-1}{5}}{r}+\frac{-1}{5}+(\frac{-1}{5})r$
which simplifies to
$\frac{-7}{10}=\frac{-1}{5r}+\frac{-1}{5}+\frac{-r}{5}$
multiply both sides by 10r
-7r=-2-2r-2r²
add (2r²+2r+2) to both sides
2r²-5r+2=0
solve using quadratic formula
for $ax^2+bx+c=0$
$x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$
so
for 2r²-5r+2=0
a=2
b=-5
c=2

$r=\frac{-(-5) \pm \sqrt{(-5)^2-4(2)(2)}}{2(2)}$
$r=\frac{5 \pm \sqrt{25-16}}{4}$
$r=\frac{5 \pm \sqrt{9}}{4}$
$r=\frac{5 \pm 3}{4}$
so
$r=\frac{5+3}{4}=\frac{8}{4}=2$ or $r=\frac{5-3}{4}=\frac{2}{4}=\frac{1}{2}$

use them to solve for the value of a
$\frac{-1}{5}=ar$
$\frac{-1}{5r}=a$
try for r=2 and 1/2
$a=\frac{-1}{10}$ or $a=\frac{-2}{5}$

test each
for a=-1/10 and r=2
a+ar+ar²= $\frac{-1}{10}+\frac{-2}{10}+\frac{-4}{10}=\frac{-7}{10}$
it works

for a=-2/5 and r=1/2
a+ar+ar²= $\frac{-2}{5}+\frac{-1}{5}+\frac{-1}{10}=\frac{-7}{10}$
it works

both have the same terms but one is simplified

the 3 numbers are $\frac{-2}{5}$ , $\frac{-1}{5}$ , and $\frac{-1}{10}$

6 0

3 years ago

Assistance if you please?

dybincka [34]

Answer:

38°

Step-by-step explanation:

a whole circle is equal to 360 degrees so if 52 +90= 142 the opposite side also equals 142 because they are clearly the same size. ED and AB are also the same sizes. if 360- (142+142) = 284. then you will have to divide 284 by 2. so 284÷2=76 and 76÷2=38°

hope you understand, I not that good at explaining things

also I don't know what the m means in mED

7 0

2 years ago

What are the answers?

madam [21]

Positive numbers is the last one

7 0

3 years ago

A random sample of 30 receipts for individuals shopping at the Community DrugStore showed the sample mean to be x-bar = $28.19 w

Triss [41]

Yes the answer to this question is B.