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Savatey [412]
3 years ago
6

If

b}{c + id} " alt=" \frac{a + ib}{c + id} " align="absmiddle" class="latex-formula">
is purely real complex number then prove that: ad=bc​
Mathematics
1 answer:
Simora [160]3 years ago
7 0

Rewrite the given number as

\dfrac{a+ib}{c+id}=\dfrac{(a+ib)(c-id)}{(c+id)(c-id)}=\dfrac{ac+bd+i(bc-ad)}{c^2+d^2}

If it's purely real, then the complex part should be 0, so that

\dfrac{bc-ad}{c^2+d^2}=0\implies bc-ad=0\implies\boxed{ad-bc}

as required.

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A worker has job offers from two companies. The information below summarizes the job offer from each company.Company A:Starting
Zanzabum

Using linear functions, we have that:

A.

For Company A: S_A(n) = 31000 + 3000n

For Company B: S_B(n) = 38000 + 2000n

B. The salaries will be the same after 7 years.

A linear function is given by:

y = mx + b

In which:

  • m is the slope, which is the rate of change.
  • b is the y-intercept, which is the initial value.

Item a:

  • For Company A, the salary starts at $31,000, with a raise of $3,000 each year. Thus, b = 31000, m = 3000, and the salary after n years is given by:

S_A(n) = 31000 + 3000n

  • For Company B, the salary starts at $38,000, with a raise of $2,000 each year. Thus, b = 38000, m = 2000, and the salary after n years is given by:

S_B(n) = 38000 + 2000n

Item b:

  • They will be the same after n years, for which:

S_A(n) = S_B(n)

Then

31000 + 3000n = 38000 + 2000n

1000n = 7000

n = \frac{7000}{1000}

n = 7

The salaries will be the same after 7 years.

A similar problem is given at brainly.com/question/24282972

7 0
3 years ago
At Centertown Middle School, 25% of the 124 students Mrs. Wade teaches buy their lunches in the cafeteria.
cluponka [151]

Out of 124 students, only 31 students are taught to buy their lunches in the cafeteria.

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

It is given that,

The 25% of 124 students are taught to buy their lunches in cafeteria.

Therefore, the total number of students taught to buy their lunches in cafeteria is 25% of 124.

<u>To find the number of students who are capable to buy lunches in cafeteria:</u>

  • Replace the % symbol into the numeric form.
  • The % is represented by 1 ÷ 100.

The 25% of 124 students is written as,

⇒ 25×(1/100)×124

⇒ (1/4)×124

⇒ 31

The number of students taught to buy lunches in the cafeteria out of 124 students is 31 students.

5 0
4 years ago
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8 0
4 years ago
Simplify the algebraic expression: 4x + 8y + 7x² + 5x – 2y.
-BARSIC- [3]

Answer:

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Step-by-step explanation:

7x² + 4x + 5x + 8y - 2y

5 0
3 years ago
Find the volume of a cylinder either enter an exact number in the terms of pi areU3.14 for pie 5 and 2
gizmo_the_mogwai [7]

Answer:

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So, the required volume of the cylinder is 384\pi \ \text{unit}^3.

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