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3 years ago

(2+3i)(1-2i) What is the product of the complex number

Mathematics

1 answer:

igomit [66]3 years ago

3 0

Answer:

(2+3i)(1-2i) = (8-i)

Step-by-step explanation:

The given complex number is :

Z = (2+3i)(1-2i)

We need to find the product of the complex number

$Z=2(1)+2(-2i)+3i(1)-6i^2\\\\=2-4i+3i-6i^2$

We know that, $i^2=-1$

$Z=2-i-6(-1)\\\\=2-i+6\\\\=8-i$

Hence, the product of the complex number is (8-i).

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Consider the following polynomial expression: 4x^5-16x^2+13x^8. Part B: What is the degree of the polynomial

Tanya [424]

Answer:

Step-by-step explanation:

Step 1: Write polynomial

4x⁵ - 16x² + 13x⁸

Step 2: Rearrange

13x⁸ + 4x⁵ - 16x²

The degree of a polynomial is the highest power. In this case, our degree would be 8 because of the x⁸ term being the largest exponent.

4 0

3 years ago

The mean salary of actuaries is LaTeX: \mu=\$100,000????=$100,000 and the standard deviation is LaTeX: \sigma=\$36,730????=$36,7

krek1111 [17]

Answer:

The lower limit of 95% confidence interval is 99002.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = $100,000

Sample mean, $\bar{x}$ = $111,000

Sample size, n = 36

Alpha, α = 0.05

Population standard deviation, σ = $36,730

First, we design the null and the alternate hypothesis

$H_{0}: \mu = \$100,000\\H_A: \mu \neq \$100,000$

We have to find the lower limit of the 95% confidence interval.

95% Confidence interval:

$\mu \pm z_{critical}\frac{\sigma}{\sqrt{n}}$

Putting the values, we get,

$z_{critical}\text{ at}~\alpha_{0.05} = 1.96$

$111000 \pm 1.96(\dfrac{36730}{\sqrt{36}} )\\\\ = 111000 \pm 11998.4667 \\= (99001.5333,122998.4667)\\ \approx (99002,122999)$

The lower limit of 95% confidence interval is 99002.

6 0

4 years ago

3/4 + 4/7 + 3/4<br>plz help

enyata [817]

Answer:

29/14

Step-by-step explanation:

Start by working out the LCM of these (or any common denominator). A common denominator for 4 and 7 is 28 cuz 4 x 7 = 28.

3/4 = 21/28

4/7 = 16/28

3/4 = 21/28

(21+16+21)/28 = 58/28 which can simplify to 29/14

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3 years ago

Read 2 more answers

A triangle can have sides whose lengths are 9cm, 16 cm, and

vodka [1.7K]

Answer: (B) 8 cm

Step-by-step explanation:

A triangle has 3 sides.

In order for it to be a triangle, the sum of sides a and b must be greater than the length of side c.

Testing (A) 7cm:

7 + 9 > 16

16 > 16

False

Testing (B) 8cm:

8+9 > 16

17 > 16

True

Testing (C) 25cm:

9 + 16 > 25

25 > 25

False

Testing (D) 26cm:

9 + 16 > 26

25 > 26

False

5 0

2 years ago

The total weight of a truck and its load is w pounds. Let /be the weight of the load . When it's empty the truck weighs 2,439 po

emmainna [20.7K]

Answer:

equation will be 2439+/=w

Step-by-step explanation:

It is pretty clear from the question, that

the weight of the load is /. and the weight of the empty truck is 2439 pounds.

It means when we load the truck with '/' pounds load, trucks weight increases and is given by

w = 2439 + /

For Example:

Suppose if load / = 1000 pounds it means weight of the truck after adding the load will be

w=2439+1000=3439 pounds.

6 0

3 years ago

Read 2 more answers