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Serhud [2]
3 years ago
7

Multiply the complex numbers: (1∕2 + 4i)2

Mathematics
2 answers:
rjkz [21]3 years ago
8 0

<em>[</em><em>I'm</em><em> </em><em>supposing</em><em> </em><em>that</em><em> </em><em>you</em><em> </em><em>have</em><em> </em><em>to</em><em> </em><em>find</em><em> </em><em>the</em><em> </em><em>value</em><em> </em><em>of</em><em> </em><em>(</em><em>1</em><em>/</em><em> </em><em>2</em><em> </em><em>+</em><em> </em><em>4i</em><em>)</em><em>²</em><em>]</em><em> </em>

Answer:

=  \frac{ - 63}{4}  + 4i

Step-by-step explanation:

we must know that

  • <em>(a + b)² = a² + b² + 2ab </em>

{( \frac{1}{2} + 4i) }^{2}  =  { (\frac{1}{2} })^{2}  +  {(4i)}^{2}  + 2 .  \frac{1}{2}   . 4i

=  \frac{1}{4}  + 16 {i}^{2}  + 4i

  • since i²= -1

= \frac{1}{4}  - 16 + 4i

=  \frac{1 - 64}{4}  + 4i

= \underline{ \frac{ - 63}{4}  + 4i}

<em>[I'm also assuming that instead of -153/4 + 4i option A says -63/ 4 + 4i.]</em>

so the answer is<u> option A.</u>

andrezito [222]3 years ago
3 0

Step-by-step explanation:

153∕4 + 8i is the correct answer

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Find the area of a triangle with sides 8 equals 5 b equals 8 and C equals 11
IceJOKER [234]
I round the answer to the second digit and get 18.33

4 0
3 years ago
How does the value of the digit 3 in the number 63,297 compare to the value of the digit 3 in the number 60,325
Iteru [2.4K]

Answer:

Step-by-step explanation:

The three in the first number is in the thousands place and in the second number the three is in the hundreds place.

4 0
3 years ago
Read 2 more answers
2. BT bisects ZABC. MZABT = 4x-16 and m CBT = 2x + 6 Find MZABT.
Paladinen [302]

Answer:

The measure of angle ABT is 28°

Step-by-step explanation:

* Lets revise the bisector of a angle

- If a ray bisects and angle that mean the ray divide the angle into

 two equal parts in measure

- Ex: if the ray BD bisects angle ABC, then the measure of angle ABD is

 equal to the measure of angle CBD

* Lets solve the problem

∵ BT bisects ∠ABC

∴ m∠ABT = m∠CBT

∵ m∠ABT = 4x - 16

∵ m∠CBT = 2x + 6

- Equate the two values

∴ 4x - 16 = 2x + 6

- Lets solve the equation by subtracting 2x from both sides and

 adding 16 to both sides

∴ 4x - 2x = 6 + 16

∴ 2x = 22 ⇒ divide both sides by 2

∴ x = 11

- Lets find the measure of angle ABT

∵ m∠ABT = 4x - 16

- Substitute x by 11

∴ m∠ABT = 4(11) - 16 = 44 - 16 = 28°

* The measure of angle ABT is 28°

6 0
3 years ago
After sitting in a refrigerator for a while, a turkey at a temperature of 34 degrees F is placed on the counter and slowly warms
Anton [14]

Answer:

  • k = 0.006
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Step-by-step explanation:

The initial temperature difference of 72 -34 = 38 °F is reduced to a difference of 72 -41 = 31 °F after 35 minutes. The exponential term in the temperature expression could have the factor ...

  (31/38)^(t/35) = e^(-kt)

Taking the natural log, we find ...

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  k = ln(38/31)/35 ≈ 0.00581711

To the nearest thousandth, this is ...

  k ≈ 0.006

Using this in the equation for temperature, we have ...

  T = 72 -38e^(-0.006t)

Filling in the desired value for t (80), we find the turkey temperature after 80 minutes to be about

  T = 72 -38e^(-.006×80) = 72 -38e^-.48 ≈ 48.49

  T ≈ 48 °F

The value of k is about 0.006, and the turkey temperature is about 48 °F.

4 0
3 years ago
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solong [7]

Answer:

y= -2x - 5

Step-by-step explanation:

You have use to slope intercept and formula to get the answer.

3 0
2 years ago
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