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harkovskaia [24]
2 years ago
12

Simplify the following expression below:

Mathematics
1 answer:
IrinaK [193]2 years ago
7 0
So, 4/3 - 2i

4/3 - 2i = 12/13 + i8/13

multiply by the conjugate: 
3 + 2i/3 + 2i
= 4(3 + 2i)/(3 - 2i) (3 + 2i)
(3 - 2i) (3 + 2i) = 13

(3 - 2i) (3 + 2i)

apply complex arithmetic rule: (a + bi) (a - bi) = a^2 + b^2
a = 3, b =  - 2
= 3^2 + (- 2)^2

refine: = 13
= 4(3 + 2i)/13

distribute parentheses:
a(b + c) = ab + ac
a = 4, b = 3, c = 2i
= 4(3) + 4(2i)

Simplify:
4(3) + 4(2i)
12    +    8i


4(3) + 4(2i)
Multiply the numbers: 4(3) = 12
= 12 + 2(4i)

Multiply the numbers: 4(2) = 8
= 12 + 8i


   12 + 8i
= 12 + 8i/13

Group the real par, and the imaginary part of the complex numbers:


Your answer is: 12/13 + 8i/13





Hope that helps!!!
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You're asking

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Simplify the following expression : 2 (2x-3)+5 (6x+1)
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The average estimated hours a person in the United States spent playing video games per year from 2002 to 2012 were 71, 80, 82,
ozzi

Answer:

Population variance 579

Population standard deviation 24

Step-by-step explanation:

The average estimated hours a person in the United States spent playing video games per year from 2002 to 2012 were 71, 80, 82, 78, 80, 91, 107, 121, 125, 131, and 142.

The population variance is given by:

\sigma^2=\frac{\sum(x-\mu)^2}{n}

\mu=\frac{71+80+82+78+80+91+107+121+125+131+142}{11}

\mu=\frac{1108}{11}

This implies that:

\sigma^2=\frac{(71-\frac{1108}{11})^2+(80-\frac{1108}{11})^2+(82-\frac{1108}{11})^2+(78-\frac{1108}{11})^2+(80-\frac{1108}{11})^2+...+(142-\frac{1108}{11})^2}{11}

\sigma^2=\frac{70006}{121} =579 to the nearest whole number

The population standard deviation is

\sigma=\frac{\sqrt{70006} }{11}=24 to the nearest whole number.

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