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Alika [10]
2 years ago
13

How to find the square root of complex numbers?? Find the square root of (6+8i) ??​

Mathematics
2 answers:
expeople1 [14]2 years ago
7 0

Answer: NaN

Step-by-step explanation: The square root of a complex number can be determined using a formula. Just like the square root of a natural number comes in pairs (Square root of x2 is x and -x), the square root of complex number a + ib is given by √(a + ib) = ±(x + iy), where x and y are real numbers.

http://www.math.com/students/calculators/source/square-root.htm

that's the website I used

You can also maybe do it on a scientific calculator?

Hope that's helpful

ivann1987 [24]2 years ago
6 0

Answer:

2 \sqrt{2}  + i \sqrt{2}

Step-by-step explanation:

The square of a complex number is a complex number. Here, we have:

{(a + bi)}^{2}  = 6 + 8i

{a}^{2}  + 2abi -  {b}^{2}  = 6  + 8i

We then have this system of equations:

{a}^{2}  -  {b}^{2}  = 6

2ab = 8

Solving this system:

ab = 4

b =  \frac{4}{a}

{a}^{2}  -  {( \frac{4}{a}) }^{2} = 6

{a}^{2}  -  \frac{16}{ {a}^{2} } = 6

{a}^{4}  - 16 =  6{a}^{2}

{a}^{4}  - 6 {a}^{2}  - 16 = 0

( {a}^{2}  - 8)( {a}^{2}  + 2) = 0

{a}^{2}   = 8

a = 2 \sqrt{2}

b =  \frac{4}{2 \sqrt{2} } =  \sqrt{2}

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Alecsey [184]

Answer:

460 miles, 1 week

Step-by-step explanation:

249 per week + 0.25 per mile

180 per week + 0.4 per mile

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3 years ago
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3 0
3 years ago
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Connecticut families were asked how much they spent weekly on groceries. Using the following data, construct and interpret a 95%
Amanda [17]

Answer:

The 95% confidence interval for the population mean amount spent on groceries by Connecticut families is ($73.20, $280.21).

Step-by-step explanation:

The data for the amount of money spent weekly on groceries is as follows:

S = {210, 23, 350, 112, 27, 175, 275, 50, 95, 450}

<em>n</em> = 10

Compute the sample mean and sample standard deviation:

\bar x =\frac{1}{n}\cdot\sum X=\frac{ 1767 }{ 10 }= 176.7

s= \sqrt{ \frac{ \sum{\left(x_i - \overline{x}\right)^2 }}{n-1} }       = \sqrt{ \frac{ 188448.1 }{ 10 - 1} } \approx 144.702

It is assumed that the data come from a normal distribution.

Since the population standard deviation is not known, use a <em>t</em> confidence interval.

The critical value of <em>t</em> for 95% confidence level and degrees of freedom = n - 1 = 10 - 1 = 9 is:

t_{\alpha/2, (n-1)}=t_{0.05/2, (10-1)}=t_{0.025, 9}=2.262

*Use a <em>t</em>-table.

Compute the 95% confidence interval for the population mean amount spent on groceries by Connecticut families as follows:

CI=\bar x\pm t_{\alpha/2, (n-1)}\cdot\ \frac{s}{\sqrt{n}}

     =176.7\pm 2.262\cdot\ \frac{144.702}{\sqrt{10}}\\\\=176.7\pm 103.5064\\\\=(73.1936, 280.2064)\\\\\approx (73.20, 280.21)

Thus, the 95% confidence interval for the population mean amount spent on groceries by Connecticut families is ($73.20, $280.21).

7 0
3 years ago
(5 1/4)÷(−2 1/2)? please help me
lisov135 [29]
-21/10 or -2&1/10 I used my calculator
4 0
3 years ago
Read 2 more answers
Secants BE and CF intersect at point D inside A. What is the measure of CDE?
Aleks04 [339]
MCE = 360 - (150 + 70 + 50)
mCE = 360 - 270
mCE = 90

<CDE = 1/2(mBE + mCE)
<CDE = 1/2(150 + 90)
<CDE = 1/2(240)
<CDE = 120

answer
<CDE = 120°
6 0
3 years ago
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