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3 years ago

Find the product of the complex number and its conjugate. 1 + 2i

2 answers:

eduard3 years ago

4 0

The answer to this question is:

Find the product of the complex number and its conjugate. 1 + 2i ??<span>(1+2i)
(1-2i)=
1^2+2^2=
5

Hoped This Helped, Trevorhardy
Your Welcome :)</span>

leva [86]3 years ago

3 0

Answer:

Step-by-step explanation:

If a complex number is defined as a+bi, then its conjugate is defined as

$\overline{z}=a-bi$

and the product of the complex number and its conjugate is

$z\overline{z}=(a+bi)(a-bi)=a^2+b^2$

The given complex number is

$z=1+2i$

The conjugate of given number is

$\overline{z}=1-2i$

The product of the complex number and its conjugate is

$(1+2i)(1-2i)=1^2+2^2=1+4=5$

Therefore, the product of the complex number and its conjugate is 5.

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In the past, 21% of all homes with a stay-at-home parent, the father is the stay-at-home parent. An independent research firm ha

Afina-wow [57]

Answer:

A sample size of 79 is needed.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

For this problem, we have that:

$\pi = 0.21$

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

What sample size is needed if the research firm's goal is to estimate the current proportion of homes with a stay-at-home parent in which the father is the stay-at-home parent with a margin of error of 0.09?

A sample size of n is needed.

n is found when M = 0.09. So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.09 = 1.96\sqrt{\frac{0.21*0.79}{n}}$

$0.09\sqrt{n} = 1.96\sqrt{0.21*0.79}$

$\sqrt{n} = \frac{1.96\sqrt{0.21*0.79}}{0.09}$

$(\sqrt{n})^{2} = (\frac{1.96\sqrt{0.21*0.79}}{0.09})^{2}$

$n = 78.68$

Rounding up to the nearest whole number.

A sample size of 79 is needed.

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3 years ago

A nursery sells English, tea, and miniature rosebushes in red, pink, yellow, and white. How many

rusak2 [61]

is this year 3 math? Its 4

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2 years ago

A || b what’s the value of X?

Anna007 [38]

<h3><u>Answer:</u></h3>

The value of x is 17.

<h3><u>Step-by-step explanation:</u></h3>

<u>We know that the lines are parallel because it is given that:</u>

a ∥ b

<u>Now, let's form an equation.</u>

=> 2x + 5 + 8x + 5 = 180

<u>Let's solve!</u>

=> 10x + 10 = 180
=> 10x = 170
=> x = 17

Hence, the value of x is 17.

$BrainiacUser1357$

4 0

2 years ago

The range of the function f(k) = k2 + 2k + 1 is {25, 64}. What is the function’s domain? {5, 8} {-5, -8} {3, 8} {4, 7} {4, 8}

Savatey [412]

The range is the ouutput from inputing the input
basically
25=k²+2k+1 and 64=k²+2k+1
the values that satisfy both equations (not at the same tim) are the valuess that are the domain
solve each
25=k²+2k+1
minus 25 both sides (or recognize the perfect square trinomial, but anyway)
0=k²+2k-24
factor
0=(k+6)(k-4)
set to zero
k+6=0
k=-6
k-4=0
k=4
k=-6 or 4

64=k²+2k+1
minus 64 both sides
0=k²+2k-63
facor
0=(k-7)(k+9)
set to zer
k-7=0
k=7
k+9=0
k=-9
k=-9 or 7

so the domain has the numbers
-9,-6,4,7
it seems we only want the positive square roots so
answer is {4,7} is the domain

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2 years ago

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lapo4ka [179]

Answer:

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Step-by-step explanation:

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2 years ago

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