1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
olga2289 [7]
3 years ago
15

Determine the modulus of each of the complex numbers in the matching pairs. List these moduli in order from smallest to largest.

Use the letters of the matching pair in your listing.
Suppose m = 2 + 6i, and |m + n| = 3√10 , where n is a complex number.

a. What is the minimum value of the modulus of n?

√10

Provide one example of the complex number, n.



A = J → 2 + 6i

B = F →75

C = H → -3 - i

D = I → 1 + i

E = G → 5 + 5i

these are my matching pairs
Mathematics
1 answer:
slava [35]3 years ago
7 0

Answer:

the modulus of a complex number z = a + bi is:

Izl= √(a²+b²)

The fact that n is complex does not mean that n doesn't has a real part, so we must write our numbers as:

m = 2 + 6i

n = a + bi

Im + nl = 3√10

√(a² + b²+ 2²+ 6²)= 3√10

√(a^2 + b^2 + 40) = 3√10

squaring both side

a²+b²+40 = 3^2*10 = 9*10 =90

a²+b²= 90 - 40

a²+b²=50

So,

|n|=√(a^2 + b^2) = √50

The modulus of n must be equal to the square root of 50.

now

values a and b such

a^2 + b^2 = 50.

for example, a = 5 and b = 5

5²+5²=25+25= 50

Then a possible value for n is:

n = 5+5i

You might be interested in
What is the solution of -8/2y-8=5/y+4 - 7y+8/y^2-16
blsea [12.9K]

Answer:

<h2>y = 8</h2>

Step-by-step explanation:

Domain:\\\\2y-8\neq0\ \wedge\ y+4\neq0\ \wedge\ y^2-16\neq0\\\\2y\neq8\ \wedge\ y\neq-4\ \wedge\ y^2\neq16\\\\y\neq4\ \wedge\ y\neq-4\ \wedge\ y\neq\pm\sqrt{16}\\\\y\neq4\ \wedge\ y\neq-4\ \wedge\ y\neq-4\ \wedge\ y\neq4\\\\\boxed{y\neq-4\ \wedge\ y\neq4}\\\\===========================

\dfrac{-8}{2y-8}=\dfrac{5}{y+4}-\dfrac{7y+8}{y^2-16}\\\\\dfrac{-8}{2(y-4)}=\dfrac{5}{y+4}-\dfrac{7y+8}{y^2-4^2}\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\\dfrac{-8}{2(y-4)}=\dfrac{5}{y+4}-\dfrac{7y+8}{(y-4)(y+4)}\qquad\text{multiply both sides by (-2)}\\\\\dfrac{8}{y-4}=-\dfrac{10}{y+4}+\dfrac{14y+16}{(y-4)(y+4)}\qquad\text{add}\ \dfrac{10}{y+4}\ \text{to both sides}\\\\\dfrac{8}{y-4}+\dfrac{10}{y+4}=\dfrac{14y+16}{(y-4)(y+4)}

\dfrac{8(y+4)}{(y-4)(y+4)}+\dfrac{10(y-4)}{(y-4)(y+4)}=\dfrac{14y+16}{(y-4)(y+4)}\\\\\dfrac{8(y+4)+10(y-4)}{(y-4)(y+4)}=\dfrac{14y+16}{(y-4)(y+4)}\qquad\text{use the distributive property}\\\\\dfrac{8y+32+10y-40}{(y-4)(y+4)}=\dfrac{14y+16}{(y-4)(y+4)}\qquad\text{combine like terms}\\\\\dfrac{(8y+10y)+(32-40)}{(y-4)(y+4)}=\dfrac{14y+16}{(y-4)(y+4)}\\\\\dfrac{18y-8}{(y-4)(y+4)}=\dfrac{14y+16}{(y-4)(y+4)}\iff18y-8=14y+16\\\\18y-8=14y+16\qquad\text{subtract 14y from both sides}

4y-8=16\qquad\text{add 8 to both sides}\\\\4y=24\qquad\text{divide both sides by 4}\\\\y=8\in D

8 0
3 years ago
The Millers must make a 70-mile Thanksgiving trip to visit their grandparents. Pat Miller believes in driving at a steady rate o
Nookie1986 [14]

Answer:

(a) 1.4 hours or 1 hour 24 minutes.

(b) 15 miles.

(c) (5/6)t  miles.

(d) 70 -  (5/6 t  miles.

Step-by-step explanation:

(a) speed =  distance / time

50 = 70 / t

t = 70/50

t = 7/5

t = 1.4 hours.

(b)  18 minutes = 18/60 = 0.3 hours.

50 = distance / 0.3

distance = 50 * 0.3

= 15 miles.

(c). 50 = d /  (t/60)

50 = 60d / t

60d = 50t

d = (5/6) t  miles.

(d)  Number of miles remaining after t minutes =  70 - (5/6) t  miles.

8 0
3 years ago
5/10 = n/40 HELP, WILL GIVE BRAINLIST IF PERFECT ANSWER
kondor19780726 [428]

Answer:

n=20

Step-by-step explanation:

5/10 equals 1/2 when simplified since 5÷5=1 and 10÷5=2

Half of 40 equals 40÷2 = 20 so n=20

Another way to do it is

Since the denominator is multiplied by 4 to get to 40

We must multiply 5 by 4 to get the numerator:

5×4=20

So n=20

3 0
2 years ago
Solve the equation below. If the solution is not an integer, give it in fractional form reduced to lowest terms.
Lina20 [59]

Answer:

x = 21

eliminate the denominator of 4

you can do this buy multiplying both sides by 4

x -9 = 12

x = 21

6 0
3 years ago
The balance of a shop owner’s bank account is $6,235.50. If the shop owner earns $430.30 on Monday, spends $3,902.50 on Tuesday,
Elenna [48]
The answer is -182.5
8 0
2 years ago
Read 2 more answers
Other questions:
  • Can someone please find the value of X for these two questions?
    9·1 answer
  • Julio wants to calculate 200,000 × 300,000. When he used his calculator to multiply, it showed the result below: Write the numbe
    12·1 answer
  • According to chebyshev's theorem, at least what percent of the observations lie within plus and minus 1.75 standard deviations o
    5·1 answer
  • Gordon was thinking of a number. Gordon doubles it and gets an answer of 90.8. What was the original number?
    13·1 answer
  • Tasty Bakery sells three kinds of muffins chocolate chip muffins at 15 cents each, oatmeal muffins at 20 cents each, and cranber
    12·2 answers
  • How to do this question
    9·1 answer
  • If ∠ECD = 45° and ∠BED = 110° is ΔABE ~ ΔCDE? If so, by what criterion? A) yes, by AA criterion B) yes, by SAS criterion C) yes,
    14·2 answers
  • Write 2.0 × 103 in standard form
    11·1 answer
  • The sum of two numbers is 9.9, and the sum of the squares of the numbers is 53.21. What are the numbers?
    9·1 answer
  • Math problem its the screen shot
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!