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Naily [24]
1 year ago
11

Perform the indicated operation and express the result as a simplified complex number. I need help with 35

Mathematics
1 answer:
skelet666 [1.2K]1 year ago
3 0

Given:-

\frac{3+4i}{2-i}

To find:-

The simplified form.

At first we take conjucate and multiply below and above.

The conjucate is,

2+i

So now we multiply. we get,

\frac{3+4i}{2-i}\times\frac{2+i}{2+i}

Now we simplify. so we get,

\frac{3+4i}{2-i}\times\frac{2+i}{2+i}=\frac{6+3i+8i+4(i)^2}{2^2-i^2}

We know the value of,

i^2=-1

Substituting the value -1. we get,

\begin{gathered} \frac{6+3i+8i+4(i)^2}{2^2-i^2}=\frac{6+3i+8i+4(-1)_{}^{}}{2^2-(-1)^{}} \\ \text{                               =}\frac{6-4+11i}{2+1} \\ \text{                              =}\frac{2+11i}{3} \end{gathered}

So now we split the term to bring it into the form a+ib. so we get,

\frac{2+11i}{3}=\frac{2}{3}+i\frac{11}{3}

So the required solution is,

\frac{2}{3}+i\frac{11}{3}

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4vir4ik [10]
96
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8 0
3 years ago
(10-3)*2+(5-14/2 help
Dafna11 [192]
2(10-3) distribute = 2*10 is 20 and 2*3 is 6
20-6+(5-14/2)
now 20-6 is 14
14+(5-14/2)
now 14/2 is 7
14+(5-7)
now 5-7 is -2
14+-2
is 12 
the answer is 12
but if you want to you can do 12/3 to get the greatest common factor 
which is 4
hope i help you :P 
6 0
3 years ago
Read 2 more answers
Please help ASAP show work^
Art [367]

Answer:x=6

Step-by-step explanation: Remove the radical by raising each side to the index of the radical

4 0
3 years ago
Your cousin renews his apartment lease and pays a new monthly rent. His new rent is calculated by applying a discount of $50 to
nasty-shy [4]

Answer:

  • $1100

Step-by-step explanation:

Let the rent be x

<u>Discounted rent </u>

  • x - $50

<u>Increase applied</u>

  • 10%

<u>Final rent:</u>

  • (x - 50) + 10% = (x - 50)*1.1

<u>We know this is equal to x + 5% = 1.05x, comparing now</u>

  • 1.1(x - 50) = 1.05x
  • 1.1x - 1.05x = 55
  • 0.05x = 55
  • x = 55/0.05
  • x = $1100
6 0
3 years ago
3x-10-4
snow_lady [41]

Answer/Step-by-step Explanation:

1. 3x - 10 +4 if x = 3

To evaluate, plug in the value of x in the expression given

3(3) - 10 + 4 = 9 - 10 + 4

= 3

2. \frac{x}{2} + 6x

if x = -12

\frac{(-12)}{2} + 6(-12)

- 6 - 72 = - 78

3. 8(x - y), if x = 2, y = 6

8(2 - 6) = 8(-4) = -32

4. x + xy, if x = 3, y = -2.5

3 + (3)(-2.5) = 3 + (-7.5)

= 3 - 7.5 = - 4.5

5. (2x)² + 6, if x = -2

(2*-2)² + 6 = (-4)² + 6

= 16 + 6 = 22

6. 3x + 4y - 3x, if x = 2, y = 4

3(2) + 4(4) - 3(2) = 6 + 16 - 6

= 16

7. -10x + \frac{4}{x}

If x = -2

-10(-2) + \frac{4}{-2}

20 + (-2) = 20 - 2 = 18

8. 3(8x - 10) + 5x, if x = ½

3(8*½ - 10) + 5(½)

3(4 - 10) + 2.5

3(-6) + 2.5 = -18+2.5 = - 20.5 or 20½

9. x + 8y - (x)², if x = -5, y = ¼

-5 + 8(¼) - (-5)² = -5 + 2 - (25)

= -3 - 25 = -28

10. (8x)² + 6x + 2, if x = -3

(8*-3)² + 6(-3) + 2 = (-24)² - 18 + 2

= 576 - 18 + 2 = 560

11. 2x² + 4y² + xy, if x = ½, y = 2

2(½)² + 4(2)² + (½)(2)

= 2(¼) + 4(4) + 1

= ½ + 16 + 1 = ½ + 17 = 17½

12. 8x + 2y, if x = 1.5, y = -2.2

8(1.5) + 2(-2.2)

12 - 4.4 = 7.6

13. \frac{5}{2}(x - 6) + 4

if x = 8.

\frac{5}{2}(8 - 6) + 4

\frac{5}{2}(2) + 4

= 5 + 4 = 9

14. 3x - 8x² + 7, if x = 4.5

3(4.5) - 8(4.5)² + 7

13.5 - 8(20.25) + 7

13.5 - 162 + 7 = -141.5

15. -2x² + 8y, if x = 3, y = -9

-2(3)² + 8(-9)

-2(9) - 72 = - 18 - 72 = 90

16. (-5x)² - 3x + x, if x = -3.5

(-5*-3.5)² - 3(-3.5) +(-3.5)

(17.5)² + 10.5 - 3.5

306.25 + 10.5 - 3.5 = 313.25

8 0
3 years ago
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