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

Mathematics

1 answer:

viva [34]3 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)

You might be interested in

How many hundredths in 1 whole

beks73 [17]

One hundred hundredths make up one whole.

8 0

3 years ago

Read 2 more answers

What is the least common denominator of 5/6 and 3/4?

ololo11 [35]

This lcd is also twelve

5 0

3 years ago

20 POINTS!!!!!

Rom4ik [11]

Answer:

5/the number of socks he has

8 0

2 years ago

A gardener already has four and one over 2 ft of fencing in his garage. He wants to fence in a square garden for his flowers. Th

NikAS [45]

<h2>Answer:</h2>

$6\frac{1}{2}$ <u>, "six and one over two ft".</u>

<h2>Step-by-step explanation:</h2>

Let's considerate the fact that the garden has a <u>square shape</u>.

<h3>1. Finding values of interest.</h3>

Amount of fence that the gardener already has: $4\frac{1}{2}$ ft.

Length of one side: $2\frac{3}{4}$ ft.

If one side measures $2\frac{3}{4}$ ft, and the square garden has 4 sides of equal length, because it's a square, then we must multiply the measure of one side by 4 to find the total length of fence needed:

$4*(2\frac{3}{4})=\\ \\4*(2+\frac{3}{4})=\\ \\(4*2)+(4*\frac{3}{4})=\\ \\8+(\frac{12}{4} )=\\ \\8+3=\\ \\11$

The gardener already has $4\frac{1}{2}$ , which equals $4 + \frac{1}{2}$ . Hence, the difference between the amount needed and the amount that the gardeneralready has will give us the remaining amount required. Let's do that: