a. Simplify 5j³(3√-25 -j⁷√-4), giving answer in the form a + bj
b. 2x + j5 - 6 = jy - j3 + 10, find values x and y
c. what us the value of x if the function f(x) = 4x² - 3x + 1 has the minimum value?
Hello Wakuiz
Welcome to Math Help Forum!(a) All you need to do here is to use the fact that and then use the ordinary rules of algebra.
So
And
Also note that and .
So
Can you complete it? I get the final answer .
(b) In this question you 'Compare reals and imaginaries'. In other words, the real parts of each side of the equation are equal, and the imaginary parts are equal.
So, reals:
Imaginaries:
I'm sure you can solve it now!
(c) This is all about handling a quadratic expression. You can do it:
- by differentiating
- by simply quoting a formula (if you know it) or
- by completing the square.
I'll show you the last method, since I'm guessing that might be the way you've been shown.
Take out factor to make coefficient of equal to :
Write half the coefficient of inside a 'bracket squared':
Subtract the square of this number, and add in the original constant number:
Simplify:
Since for all real values of , you can then say that the value of is a minimum when ; i.e. when .
Grandad