Given:-
![\frac{3+4i}{2-i}](https://tex.z-dn.net/?f=%5Cfrac%7B3%2B4i%7D%7B2-i%7D)
To find:-
The simplified form.
At first we take conjucate and multiply below and above.
The conjucate is,
![2+i](https://tex.z-dn.net/?f=2%2Bi)
So now we multiply. we get,
![\frac{3+4i}{2-i}\times\frac{2+i}{2+i}](https://tex.z-dn.net/?f=%5Cfrac%7B3%2B4i%7D%7B2-i%7D%5Ctimes%5Cfrac%7B2%2Bi%7D%7B2%2Bi%7D)
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}](https://tex.z-dn.net/?f=%5Cfrac%7B3%2B4i%7D%7B2-i%7D%5Ctimes%5Cfrac%7B2%2Bi%7D%7B2%2Bi%7D%3D%5Cfrac%7B6%2B3i%2B8i%2B4%28i%29%5E2%7D%7B2%5E2-i%5E2%7D)
We know the value of,
![i^2=-1](https://tex.z-dn.net/?f=i%5E2%3D-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}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cfrac%7B6%2B3i%2B8i%2B4%28i%29%5E2%7D%7B2%5E2-i%5E2%7D%3D%5Cfrac%7B6%2B3i%2B8i%2B4%28-1%29_%7B%7D%5E%7B%7D%7D%7B2%5E2-%28-1%29%5E%7B%7D%7D%20%5C%5C%20%5Ctext%7B%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%3D%7D%5Cfrac%7B6-4%2B11i%7D%7B2%2B1%7D%20%5C%5C%20%5Ctext%7B%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%3D%7D%5Cfrac%7B2%2B11i%7D%7B3%7D%20%5Cend%7Bgathered%7D)
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}](https://tex.z-dn.net/?f=%5Cfrac%7B2%2B11i%7D%7B3%7D%3D%5Cfrac%7B2%7D%7B3%7D%2Bi%5Cfrac%7B11%7D%7B3%7D)
So the required solution is,
Answer: C
Step-by-step explanation:
-100-_= 45
-100+145= 45
Negative plus negative equals a positive sign
Answer:
27 is a cubed number because 3 to the third power, or cubed, is 27. 3*3*3=27. 3*3=9.
9*3=27
Step-by-step explanation:
Answer:
x=22
Step-by-step explanation:
Rule states diagonals = same so 6x-36 = 96 in which x=22 cause 6(22)=132
132-36 = 96
4(a + 2) + 9 = 5
to solve this problem lets solve this step by step
Step 1 - lets solve this part of problem 4(a + 2 )
by using distributive property we get,
4a + 8 + 9 = 5
Step 2 - adding the like terms
4a + 17 = 5
Step 3 - subtracting 17 from both sides
4a + 17 - 17 = 5 - 17
4a = -12
Step 4 - dividing both sides by 4
a = -3
So our final answer is a = -3
Hope this helps you :)