Answer:
The answer to this question is -11
Answer: (28/37) - (48/37)*i
Step-by-step explanation:
We want to solve the quotient:
![\frac{6 - 7*i}{6 + i}](https://tex.z-dn.net/?f=%5Cfrac%7B6%20-%207%2Ai%7D%7B6%20%2B%20i%7D)
To solve it, we need to multiply the whole quotient by the complex conjugate of the denominator.
Remember that for a complex number:
a + b*i
the complex conjugate is:
a - b*i
Then if the denominatoris:
6 + i
the complex conjugate is:
6 - i
Then to solve the quotient we have:
![\frac{6 - 7*i}{6 + i} *\frac{6 - i}{6 - i} = \frac{(6 -7*i)*(6 - i)}{(6 + i)*(6 - i)} = \frac{6*6 -7*6*i - 6*i + (-7*i)*(-i)}{6*6 +6*i - 6*i -i^2}](https://tex.z-dn.net/?f=%5Cfrac%7B6%20-%207%2Ai%7D%7B6%20%2B%20i%7D%20%2A%5Cfrac%7B6%20-%20i%7D%7B6%20-%20i%7D%20%3D%20%20%5Cfrac%7B%286%20%20-7%2Ai%29%2A%286%20-%20i%29%7D%7B%286%20%2B%20i%29%2A%286%20-%20i%29%7D%20%3D%20%5Cfrac%7B6%2A6%20-7%2A6%2Ai%20-%206%2Ai%20%2B%20%28-7%2Ai%29%2A%28-i%29%7D%7B6%2A6%20%2B6%2Ai%20-%206%2Ai%20-i%5E2%7D)
This is equal to:
![\frac{6*6 -7*6*i - 6*i + (-7*i)*(-i)}{6*6 +6*i - 6*i -i^2} = \frac{36 - 42*i - 6*I - 7}{36 + 1} = \frac{29 - 48*i}{37}](https://tex.z-dn.net/?f=%5Cfrac%7B6%2A6%20-7%2A6%2Ai%20-%206%2Ai%20%2B%20%28-7%2Ai%29%2A%28-i%29%7D%7B6%2A6%20%2B6%2Ai%20-%206%2Ai%20-i%5E2%7D%20%3D%20%5Cfrac%7B36%20-%2042%2Ai%20-%206%2AI%20-%207%7D%7B36%20%2B%201%7D%20%20%3D%20%5Cfrac%7B29%20-%2048%2Ai%7D%7B37%7D)
Then the initial quotient is equal to:
(28/37) - (48/37)*i
The inverse is just switching y and x your answer should be . p^-1 (m)=5m-40
Real numbers are compared by distance from zero. So you have to convert numbers to decimals to find which number is greater.
To have infinite solutions both equations need to be equal
Since they subtract 5 from the right side, subtract 5 from the left side.
X is multiplied by 1/2 on the left , so multiply x by 1/2 on the right side.
1/2x -5 = 1/2x-5