I forgot some stuff from my 7th grade algebra class about complex numbers...like what do you do with a problem like this
5+5i 3-i
divided by + divided by
2-i 4+3i
thanks.(divided by refers to dividing line in a fraction)
In each case, RATIONALIZE the denominator. Here is the way on the first problem. Mulitipy the numerator and the demoniator by 2+1. Isn't that called the complex conjugate? Anyway, that will solve the problem.
Then multiply on the second fraction both top and bottom by the complex conjugate, 4-3i, simplify all, and you are done.
2x squaed plus 27 equal 0
7/8 x 6/7 =
To solve the problem involving complex numbers, you'll need to perform division and rationalize the denominator. Here's how you can approach it step by step:
1. Simplify the complex fractions separately.
2. In the first fraction (numerator and denominator), multiply both the numerator and denominator by the complex conjugate of the denominator. The complex conjugate is formed by changing the sign of the imaginary part.
In this case, the complex conjugate of 2 - i is 2 + i.
(5 + 5i) / (2 - i) becomes [(5 + 5i) * (2 + i)] / [(2 - i) * (2 + i)]
Multiply the numerators together and the denominators together to get the new fraction.
The numerator is (5 + 5i) * (2 + i) = 10 + 10i + 5i + 5i^2 = 10 + 15i + 5i^2 = 10 + 20i + 5i^2
Simplify the terms: 10 + 20i + 5i^2 = 10 + 20i - 5 (since i^2 = -1) = 5 + 20i.
The denominator is (2 - i) * (2 + i) = 4 + 2i - 2i - i^2 = 4 - i^2 = 4 - (-1) = 4 + 1 = 5.
Hence, the first fraction simplifies to (5 + 20i) / 5 = (1 + 4i).
3. In the second fraction (numerator and denominator), again multiply both the numerator and denominator by the complex conjugate of the denominator, which is 4 - 3i.
(3 - i) / (4 + 3i) becomes [(3 - i) * (4 - 3i)] / [(4 + 3i) * (4 - 3i)]
Multiply the numerators together and the denominators together.
The numerator is (3 - i) * (4 - 3i) = 12 - 9i - 4i + 3i^2 = 12 - 13i + 3i^2
Simplify the terms: 12 - 13i + 3i^2 = 12 - 13i - 3 (since i^2 = -1) = 9 - 13i.
The denominator is (4 + 3i) * (4 - 3i) = 16 + 12i - 12i - 9i^2 = 16 - 9i^2 = 16 - (-9) = 16 + 9 = 25.
Hence, the second fraction simplifies to (9 - 13i) / 25.
4. Now that you have simplified both fractions, you can divide them by each other.
(1 + 4i) / (9 - 13i) = (1 + 4i) * (25 / (9 - 13i))
Multiply the numerators together and the denominators together.
The numerator is (1 + 4i) * 25 = 25 + 100i.
The denominator remains the same: (9 - 13i).
Therefore, the final simplified result is (25 + 100i) / (9 - 13i).
Regarding the second part of your question, "2x squared plus 27 equal to 0," it seems to be a quadratic equation. However, the equation needs to be set to 0 before solving it. If you have the correct equation, I can explain further and help you with it.
Finally, for the expression "7/8 x 6/7," you can simply multiply the numerators together and the denominators together to get the result.
(7/8) * (6/7) = (7 * 6) / (8 * 7) = 42 / 56 = 3/4.
If you have any other questions or need further assistance, feel free to ask!