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Pavlova-9 [17]
3 years ago
9

How would you simplify (3+i)(4+2i)?​

Mathematics
2 answers:
const2013 [10]3 years ago
7 0

Answer:

<h2>(3 + i)(4 + 2i) = 10 + 10i</h2>

Step-by-step explanation:

Use FOIL: (a + b)(c + d) = ac + ad + bc + bd

and i² = -1

(3+i)(4+2i)\\\\=(3)(4)+(3)(2i)+(i)(4)+(i)(2i)\\\\=12+6i+4i+2i^2\qquad\text{combine like terms}\\\\=(12-2)+(6i+4i)\\\\=10+10i

Lunna [17]3 years ago
7 0

Answer:

11 + 10i

Step-by-step explanation:

Note that we're multiplying two binomials here, and thus may use the FOIL method.  This requires four multiplications, as follows:

3*4 + 3*2i + 4i - 1               (The last term is 1 because i(i) = i^2 = -1.)

Simplifying, we get:

12 + 6i + 4i -1, or:

11 + 10i

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A circle with radius \pink{6}6start color #ff00af, 6, end color #ff00af has a sector with a central angle of \purple{48^\circ}48
alexandr1967 [171]

Answer:

Therefore,

The area of the sector is 15.09 unit².

Step-by-step explanation:

Given:

Circle with,

radius = r = 6 unit

central angle = θ = 48°

pi = 3.143

To Find:

Area of sector = ?

Solution:

If  'θ' is in degree the area of sector is given as

\textrm{Area of Sector}=\dfrac{\theta}{360}\times \pi r^{2}

Substituting the values we get

\textrm{Area of Sector}=\dfrac{48}{360}\times 3.143\times 6^{2}

\textrm{Area of Sector}=15.0864=15.09\ unit^{2} rounded to nearest hundredth

Therefore,

The area of the sector is 15.09 unit².

7 0
3 years ago
Read 2 more answers
What is the equation of a line with a y-intercept at (0,6) and a slope of 3?
tino4ka555 [31]

Answer: answer A

Step-by-step explanation: y = mx + b

8 0
3 years ago
Help me with this please
Reika [66]

Answer:

$2,459.21

Step-by-step explanation:

(see attached for reference)

recall that the formula for compound interest is:

A = P [ 1 + (r/n)^ (nt) ]

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r = Annual Interest Rate = given as 5% = 0.05

n = number of times compounded in a year = 4 (compounded quarterly)

t= time = 1 year

Substituting the values into the equation,

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A = $2,459.21

6 0
3 years ago
143=7+8(3-7x) solve and justify
Llana [10]
Justify means plug answer in and verify

so distribute 8(3-7x)=24-56x

143=7+24-56x
143=31-56x
minus 31 both sides
112=-56x
divide both sides by -56
-2=x

justify

plug it back
143=7+8(3-7x)
143=7+8(3-7(-2))
143=7+8(3-(-14))
143=7+8(3+14)
143=7+8(17)
143=7+136
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true

x=-2

7 0
3 years ago
Using an ordered alphabet of 26 letters, how many ways are there to choose a set of six letters such that no two letters in the
mestny [16]
To find our solution, we can start off by creating a string of 27 boxes, all followed by the letters of the alphabet. Underneath the boxes, we can place 6 pairs of boxes and 15 empty boxes.The stars represent the six letters we pick. The empty boxes to the left of the stars provide the "padding" needed to ensure that no two adjacent letters are chosen. We can create this - 
\binom {21} {6}= \frac{21*20*19*18*17*16}{6*5*4*3*2*1} =21*19*17*8=54264
Thus, the answer is that there are \boxed{54264} ways to choose a set of six letters such that no two letters in the set are adjacent in the alphabet. Hope this helped and have a phenomenal New Year! <em>2018</em>
5 0
3 years ago
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