The product of a <em>complex</em> number and its conjugate is (a + i b) · (a - i b), where a and b are <em>real</em> numbers, and the result for the <em>complex</em> number 2 + i 3 is 13.
<h3>What is the multiplication of a complex number and its conjugate</h3>
Let be a <em>complex</em> number a + i b, whose conjugate is a - i b. Where a and b are <em>real</em> numbers. The product of these two numbers is:
(a + i b) · (a - i b)
Then, we proceed to obtain the result by some algebraic handling:
a · (a + i b) + (- i b) · (a + i b)
a² + i a · b - i a · b - i² b²
a² - i² b²
a² + b²
If we know that a = 2 and b = 3, then the product of the complex number and its conjugate is:
To learn more on complex numbers: brainly.com/question/10251853
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Answer:
The answer is 166
Step-by-step explanation:
x+90+24
Expected value of the bet is
the sum of the products of value of outcome and its probability,
less the amount paid to place the bet.
Outcomes value probability
win 225 1/4
lose 0 3/4
cost of bet = 40
So expected value of bet
E[X]=225*(1/4)+0*(3/4)-40
=56.25-40
=16.25
This means that in the long run, gambler will win, since the expected value is positive. (does NOT mean she will win in the next bet!)