Simplify the expression

Mathematics

1 answer:

AlexFokin [52]3 years ago

5 0

Answer:

Step-by-step explanation:

$\frac{3+4\iota}{2+4\iota}=\frac{3+4 \iota}{2+4\iota} \times \frac{2-4 \iota}{2-4 \iota}\\=\frac{6 -12 \iota+8 \iota-16 \iota^2 }{4-16 \iota^2 }\\=\frac{ 6-4 \iota+16}{4+16}\\=\frac{22-4 \iota}{20}$

You might be interested in

Alaina has $28 in her account. She wants to purchase a pair of shoes that costs $45. If Alaina makes the purchase, which integer

valentina_108 [34]

Answer:

The Integer is -17

Step-by-step explanation:

This is because you must subtract the cost of the shoes from her account

28 - 45 is equal to negative 17

4 0

3 years ago

A teacher was interested in knowing the amount of physical activity that his students were engaged in daily. He randomly sampled

klasskru [66]

Answer:

The standard error of the mean is 4.5.

Step-by-step explanation:

As we don't know the standard deviation of the population, we can estimate the standard error of the mean from the standard deviation of the sample as:

$\sigma_{\bar{x}}\approx\frac{s}{\sqrt{n}}$

The sample is [30mins, 40 mins, 60 mins, 80 mins, 20 mins, 85 mins]. The size of the sample is n=6.

The mean of the sample is:

$\bar{x}=\frac{1}n} \sum x_i =\frac{30+40+60+80+20+85}{6}=52.5$

The standard deviation of the sample is calculated as:

$s=\sqrt{\frac{1}{n-1}\sum (x_i-\bar x)^2} \\\\ s=\sqrt{\frac{1}{5}\cdot ((30-52.5)^2+(40-52.5)^2+(60-52.5)^2+(80-52.5)^2+(20-52.5)^2+(85-52.5)^2}\\\\s=\sqrt{\frac{1}{5} *3587.5}=\sqrt{717.5}=26.8$