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4 years ago

Which pair of complex numbers has a real-number product? (1 + 2i)(8i) (1 + 2i)(2 – 5i) (1 + 2i)(1 – 2i) (1 + 2i)(4i)

Mathematics

2 answers:

kupik [55]4 years ago

5 0

Answer:

(1+2i)(1-2i)

Step-by-step explanation:

vlabodo [156]4 years ago

5 0

Answer:

(1+2i)(1-2i)

Step-by-step explanation:

Following are the pairs of the complex number:

(1+2i)(8i),

(1 + 2i)(2 – 5i)

(1+2i)(1-2i) and (1+2i)(4i)

We have to check which pair out of these is a real number product, which means which pair do not contain terms consisting of "i".

A. $(1+2i)(8i)= 8i+16i^{2}$

= $8i-16$

B. $(1+2i)(2-5i)=2-i-10i^{2}$

= $12-i$

C. $(1+2i)(1-2i)=1^{2}-4i^{2}$

= $5$

D. $(1+2i)(4i)=4i+8i^{2}$

= $4i-8$

Since, A,B,D contains the term "i" which means they are not real valued, therefore option C that is (1+2i)(1-2i) has a real number product.

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What is the remainder of the following division problem? x startlongdivisionsymbol x 1 endlongdivisionsymbol. minus x to get a r

irga5000 [103]

The remainder of the expression x/(x + 1) is a negative one. Then the correct option is D.

<h3>What is division?</h3>

The division means the separation of something into different parts, sharing of something among different people, places, etc.

The expression is given below.

$\rm \rightarrow \dfrac{x}{x+1}$

Add and subtract 1 in the numerator, then we have

$\rm \rightarrow \dfrac{x+1-1}{x+1}\\\rm \rightarrow 1 -\dfrac{1}{x+1}$

Then the remainder will be a negative one.

More about the division link is given below.

brainly.com/question/369266

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2 years ago

REPOST OF GEOMETRY QUESTION !!

sergiy2304 [10]

$r^2=(11.7)^2-10^2\\
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7 0

3 years ago

Help pls need help show your solution and then graph

Stella [2.4K]

Answer:

Step-by-step explanation:

We can use the quadratic formula or factor, This looks hard to factor so we should use the quadratic formula.

ax^2 + bx + c

a=4

b=-9

c=2

you can try it by hand or use this:

https://www.calculatorsoup.com/calculators/algebra/quadratic-formula-calculator.php

you get x=2 and x=0.25 these are the x intercepts (where Y is zero and where the graph crosses the x axis)

so mark x=2 and x=0.25 with a dot on a number line and you can draw a straight line between them since that is the part of the graph that is below the x axis (because the equation has <0) it is a positive parabola because the "a" value is positive and the presence of a "b" value means part of the graph will be below the x axis

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2 years ago

A computer program has a bug that causes it to fail once in every thousand runs, on average. In an effort to find the bug, indep

Serhud [2]

Answer:

The standard deviation of the number of runs required is 2447.26

Step-by-step explanation:

For each run, there are only two possible outcomes. Either the program fails, or it does not. The probability of the computer failing during a run is independent of other runs. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The standard deviation for the expected number of trials for r sucesses is:

$\sqrt{V(X)} = \sqrt{\frac{r(1-p)}{p^{2}}}$

A computer program has a bug that causes it to fail once in every thousand runs, on average.

This means that $p = \frac{1}{1000} = 0.001$

In an effort to find the bug, independent runs of the program will be made until the program has failed six times. What is the standard deviation of the number of runs required?

This means that r = 6. So

$\sqrt{V(X)} = \sqrt{\frac{6*0.999}{(0.001)^{2}}} = 2447.26$