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4 years ago

Which complex number is the simplified form of 2+5i3+i2+5i3+i?

Mathematics

1 answer:

viva [34]4 years ago

8 0

Answer:

Option (1)

Step-by-step explanation:

The given complex number is (2+5i)/(3+i)

multiplying the numerator and the denominator by the conjugate of (3+i) which is (3-i)

The denominator = (3+i)(3-i) = 3² - i² = 9 - (-1) = 10

The numerator = (2 + 5 i ) ( 3 - i ) = 2(3-i) + 5i (3 - i)

= 6 - 2i + 15 i - 5 i²

= 6 + 13 i + 5 = 11 + 13 i

So, the given complex number can be simplified to ( 11 + 13i)/10

Distributing numerator over denominator.

The simplified number = (11/10) + (13/10) i

The answer is option (1)

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What is the measure of angel R ? pls i need help

matrenka [14]

Answer:

Step-by-step explanation:

(120 - 40)/2 = 80/2 = 40

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3 years ago

For the geometric series given by 5 + 10 + 20+ . . . , which of the following statements is FALSE?

slava [35]

Answer:

All statements are true

Step-by-step explanation:

1. The statement $S_{500}>S_{499}$ is true, because $S_{499}$ is the sum of first 499 terms, $S_{500}$ is the sum of first 500 terms, and all these terms are positive, then the sum of smaller number of terms is less than the sum of larger number of terms.

2. The statement $S_{500}>a_{500}$ is true, because $S_{500}$ is the sum of first 500 terms, $a_{500}$ is 500th term and the sum of 500 terms is greater than the 500th term.

3. The statement $S_1=a_1$ is true, because $S_1$ is the sum of first 1 term that is exactly $a_1.$

All statements are true.

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4 years ago

The average value of two positive numbers is 30% less than one of the two numbers. By which percentage is average value bigger t

Viefleur [7K]

Answer:

75% bigger

Step-by-step explanation:

Let the first number be x and the second be y.

So:

$Average = \frac{x + y}{2}$

And:

$Average = (1 - 30\%) * x$ -----30% less than x

Substitute $Average = (1 - 30\%) * x$ in $Average = \frac{x + y}{2}$

$\frac{x + y}{2} = (1 - 30\%) * x$

$\frac{x + y}{2} = (1 - 0.30) * x$

$\frac{x + y}{2} = 0.70 * x$

$\frac{x + y}{2} = 0.70x$

Cross multiply

$x + y = 0.70x * 2$

$x + y = 1.40x$

Collect like terms

$1.40x - x = y$

$0.40x = y$

Make x the subject

$x = \frac{y}{0.40}$

$x = 2.50y$

So, the average is:

$Average = (1 - 30\%) * x$

$Average = (1 - 30\%) * 2.50y$

$Average =0.70 * 2.50y$

$Average =1.75y$

Rewrite as:

$Average =(1 + 0.75)y$

Express as percentage

$Average =(1 + 75\%)y$

This means that the average is 75% bigger than the second number

6 0

3 years ago

3. The talent show committee sold a total of 522 tickets. Student tickets cost $3 each and adult tickets

irina1246 [14]

Answer:

Step-by-step explanation:

If student ticket = 215 then 215 x 3 = 645$

Remaining tickets = 522 - 215 = 307

So adult tickets = 307 x 4 = 1228$

Total amount = 1228 + 645 = $1873

7 0

3 years ago

What is 1 3/7 as an improper and equivalent fraction?

Alex777 [14]

Improper: multiple the 1 by the denominator 1x7 = 7 then add to numerator number.

Final answer is 10/7

And equivalent fraction could be anything as long as it’s equal to the original.

Possible could be 1 9/21

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3 years ago