2x-3yi=14+12i how do I find x and y
2 answers:
Answer:
The answers are:
Step-by-step explanation:
In order to determine the answer, we have to know about complex numbers.
The complex numbers have one difference respect on real numbers, they have an imaginary unit .
In general, a complex number has the next form:
"a" and "b" are real numbers.
We can not add the imaginary part (where it is the imaginary unit) with the real part.
In this case, we have an equality, where in the right side, we can see a complex number and in the left side, we can see two variables and the imaginary unit. We just have to build two equation: one for the real part and other one for the imaginary part.
Finally, the values of the variables to fulfil the equality are:
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Answer:
x = √17 and x = -√17
Step-by-step explanation:
We have the equation:
To solve this we need to remove the denominators.
Then we can first multiply both sides by (x + 4) to get:
Now we can multiply both sides by (x + 3)
Now we can multiply both sides by (x^2 + 7*x + 12)
Now we need to solve this:
we will get
Then we get:
So now we only need to solve this.
We can see that the constant is 51.
Then one root will be a factor of 51.
The factors of -51 are:
-3 and -17
Let's try -3
p( -3) = (-3)^3 + 3*(-3)^2 + +17*(-3) + 51 = 0
Then x = -3 is one solution of the equation.
But if we look at the original equation, x = -3 will lead to a zero in one denominator, then this solution can be ignored.
This means that we can take a factor (x + 3) out, so we can rewrite our equation as:
The other two solutions are when the other term is equal to zero.
Then the other two solutions are given by:
x = ±√17
And neither of these have problems in the denominators, so we can conclude that the solutions are:
x = √17 and x = -√17