solve and simplify the answer completely by using pure imaginary numbers/complex numbers.
2x^2+3x+2=0
Use the quadratic formula. The one with sqrt(b^2-4ac) in it. It must be in your text. If it isn't, read
http://en.wikipedia.org/wiki/Quadratic_equation
a = 2, b = 3, c = 2
To solve the quadratic equation 2x^2 + 3x + 2 = 0 using complex numbers, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, a = 2, b = 3, and c = 2.
Plugging in these values, we have:
x = (-(3) ± √((3)^2 - 4(2)(2))) / (2(2))
= (-3 ± √(9 - 16)) / 4
= (-3 ± √(-7)) / 4
Now, we need to simplify the expression √(-7). Since the square root of a negative number is not a real number, we can express it using the imaginary unit, i, where i^2 = -1.
√(-7) = √(7) * √(-1) = √(7) * i
Now we can substitute this back into the equation:
x = (-3 ± √(7) * i) / 4
So the two solutions to the quadratic equation using pure imaginary numbers are:
x1 = (-3 + √(7) * i) / 4
x2 = (-3 - √(7) * i) / 4
This fully simplifies the equation using complex numbers.