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
zubka84 [21]
3 years ago
15

Simplify the complex number. Express your answer in a + bi form and include each step necessary in simplifying.

/tex.z-dn.net/?f=%20%5Cfrac%7B3-2i%7D%7B1%2B4i%7D%20" id="TexFormula1" title=" \frac{3-2i}{1+4i} " alt=" \frac{3-2i}{1+4i} " align="absmiddle" class="latex-formula">
Mathematics
1 answer:
insens350 [35]3 years ago
3 0
\dfrac{x+iy}{u+iv}\times\dfrac{u-iv}{u-iv}=\dfrac{(x+iy)(u-iv)}{u^2-(iv)^2}
=\dfrac{xu-i^2yv+iyu-ixv}{u^2+v^2}
=\underbrace{\dfrac{xu+yv}{u^2+v^2}}_a+i\underbrace{\dfrac{yu-xv}{u^2+v^2}}_b
You might be interested in
In AKLM, m = 1.2 cm, k = 5.1 cm and
Elodia [21]

Answer:

  4.2 cm

Step-by-step explanation:

The law of cosines is applicable.

  l² = k² +m² -2km·cos(L)

  l² = 5.1² +1.2² -2·5.1·1.2·cos(35°) ≈ 17.4236

  l ≈ √17.4236

  l ≈ 4.2 . . . cm

4 0
3 years ago
What is the area of a rectangle if the length is 5 inches and the width is 2/5
Lynna [10]
5/1 • 2/5 = 10/5 = 2

The area is 2 inches
8 0
3 years ago
The cost of a unit is made up of $6.25 material cost, $4.75 labour cost, and $3.25 overhead. What is the ratio that exists betwe
blsea [12.9K]

Answer:

The ratio that exist between this three elements are 25 : 19 : 13.

Step-by-step explanation:

Ratio compares one thing to another. Ratios indicate the comparison of the size of a number to another . One trick about ratio is that you can multiply or divide the ratios by same number. For example the ratio of boy to girls can be represented as 3 : 4. If you multiply the ratios by 2 you will get the ratio 6 : 8 and it still represent the same ratios of boys to girls. Ratios can be written as a fraction for example 3/4 for our example.

The cost of the unit is made up of $6.25 , $4.75 and $3.25.

$6.25  $4.75  $3.25 . Let us multiply by 100 to remove the decimals.

625 : 475 : 325 . Now let simplify the ratios by dividing through by 25.

625/25 : 475/25 : 325/25 . The simplest ratios can be written as follows

The ratios are 25 : 19 : 13.

6 0
3 years ago
Select all the expressions that equal.. *see picture for problem* ​
kupik [55]

Answer:

Step-by-step explanation:

oknjbgfkdfrgn jnfbfl

7 0
2 years ago
How to graph x+y=1 & is it linear
liq [111]

Answer:

Step-by-step explanation:

Plot the points x-intercept and intercept on the graph. Join the two points to get the straight line. This is the graph of the linear equation.

7 0
2 years ago
Other questions:
  • On a scale drawing of a park, the sand box is 2 inches wide. The actual sand box is 8 feet wide. What is the scale of the drawin
    10·1 answer
  • Determine which postulate or theorem can be used to prove that LMN NOL
    10·2 answers
  • What is the rate of change of the line
    5·2 answers
  • The graph of a function is shown below
    6·1 answer
  • PLEASE HELP ASAP!!!!! The following graph shows a proportional relationship. What is the constant of proportionality between y a
    7·2 answers
  • Container X has 2 cups of water with 6 teaspoons of sugar. Container Y has 4 cups of water with 8 teaspoons of sugar. In which c
    10·1 answer
  • Helpppp hurry and no links please
    9·1 answer
  • What is the volume of the cylinder shown below? A. 12157 units B. 3617 units C. 647 units D. 152 T units
    7·1 answer
  • Can you help me understand this?
    7·1 answer
  • AB=AD. Enter the range of values for x. 40° 14° 9x-27 108. ?
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!