All categories

3 years ago

(5-2i)+(3+4i)-(-6+2i)

Mathematics

1 answer:

pav-90 [236]3 years ago

3 0

Simplify

5 - 2i + 3 + 4i - (-6 + 2i)

Simplify brackets

5 - 2i + 3 + 4i + 6 - 2i

Collect like terms

(5 + 3 + 6) + (-2i + 4i - 2i)

Simplify

= 14

You might be interested in

Gena attached a dog ramp to her sofa, which allows her oldest dog to easily climb onto a seat cushion. The ramp is 55 inches lon

matrenka [14]

The distance from the base of the ramp to the base of the sofa rounded to the nearest tenth is 47.3 inches.

Explanation

According to the diagram, length of the ramp is, $AC= 55$ inches. The top of the seat cushion is 28 inches above the floor. That means, $BC=28$ inches

We need to find the distance from the base of the ramp to the base of the sofa which is $AB$

In right angle triangle $ABC$ , using Pythagorean theorem...

$AC^2 = AB^2 + BC^2\\ \\ (55)^2= AB^2 + (28)^2 \\ \\ AB^2 = (55)^2 - (28)^2 \\ \\ AB^2 = 3025 - 784\\ \\ AB^2 = 2241\\ \\ AB = \sqrt{2241}= 47.3$

So, the distance from the base of the ramp to the base of the sofa rounded to the nearest tenth is 47.3 inches.

4 0

3 years ago

Read 2 more answers

Which of these number sentences is not true

andrew-mc [135]

4,ooo,ooo mm equal 4km

6 0

3 years ago

The sum of 30 times (1/3)^(n-1) from 1 to infinity

sergeinik [125]

Let

$S_n=\displaystyle1+\frac13+\frac1{3^2}+\cdots+\frac1{3^n}$

Then

$\dfrac13S_n=\displaystyle\frac13+\frac1{3^2}+\frac1{3^3}+\cdots+\frac1{3^{n+1}}$

and

$S_n-\dfrac13S_n=\dfrac23S_n=1-\dfrac1{3^{n+1}}\implies S_n=\dfrac32-\dfrac1{2\cdot3^n}$

and as $n\to\infty$ , we end up with

$\displaystyle\lim_{n\to\infty}S_n=\lim_{n\to\infty}\sum_{i=1}^{n+1}\frac1{3^{i-1}}=\lim_{n\to\infty}\left(\frac32-\frac1{2\cdot3^n}\right)=\frac32$

So we have

$\displaystyle\sum_{n=1}^\infty30\left(\frac13\right)^{n-1}=30\cdot\frac32=45$

8 0

3 years ago

Solve this into y=mx+b form. Please help me with the steps. Thank you

kati45 [8]

Answer:

y = 4x - 3

Explanation:

4x – y + 6 = 9 Subtract 6 from each side

4x – y = 3 Subtract 4x rom each side

-y = -4x + 3 Multiply each side by -1

y = 4x - 3

6 0

4 years ago

What is the factor of 32 and 50

Dahasolnce [82]

2 is the GCF of 32 and 50.

7 0

3 years ago

Read 2 more answers