(4 – 2i)(6 + 2i)
Use FOIL
First: 4 multiplied by 6 equals 24
Outer: 4 times 2i gives 8i
Inner: -2i times 6 results in -12i
Last: -2i times 2i equals -4i², which simplifies to 4
Combine the results
24 + 8i - 12i + 4
Final result: 28 - 4i
The answer is: 28 - 4i
This problem can be addressed by applying the normal approximation to a binomial distribution.
Calculations:
Mean (μ) = np = 10,000 × 0.5 = 5,000
The standard deviation (σ) is given by:


The probability of obtaining more than 5,100 tails is 0.0228, whereas the probability of fewer than 5,100 tails is 0.9772.
Thus, the odds of having more than 5,100 tails are:
0.0228 : 0.9772 = 1 : 42.86.
The task requires calculating the coefficient of the squared term in the parabolic equation, and based on my calculations and analysis, I found that the vertex of the parabola can be expressed as y =a(x-h)^2+k, leading me to a simplification that results in x^2.