Question

Multiply (2 + 3𝑖)(4 − 𝑖

105

likes

526 views

Answer to a math question Multiply (2 + 3𝑖)(4 − 𝑖

$Expert avatar$

Hermann

4.6

126 Answers

Solution:
1. Given complex numbers:
-

a = 2 + 3i

b = 4 - i

2. Perform the multiplication using the distributive property (FOIL method):
- Multiply the first terms:

2 \cdot 4 = 8

- Multiply the outer terms:

2 \cdot (-i) = -2i

- Multiply the inner terms:

3i \cdot 4 = 12i

- Multiply the last terms:

3i \cdot (-i) = -3i^2

3. Simplify the expression:
- Combine like terms:

8 - 2i + 12i - 3i^2

- Note that

i^2 = -1

, so

-3i^2 = 3

4. Simplify further:
-

8 + 10i + 3

- Combine the real parts:

8 + 3 = 11

- Final expression:

11 + 10i

The product of the complex numbers is

11 + 10i

Frequently asked questions (FAQs)

What is the period of the trigonometric function y = sin(3x) - cos(2x)?

What is the cosine value of an angle in the unit circle whose measure is 30 degrees?

Question: What is the absolute value of the complex number (3 + 4i) multiplied by its conjugate?

New questions in Mathematics

8x²-30x-10x²+70x=-30x+10x²-20x²

The patient is prescribed a course of 30 tablets. The tablets are prescribed “1 tablet twice a day”. How many days does a course of medication last?

How do you think the company has increased or decreased its income?

Consider numbers from 1 to 2023. We delete 3 consecutive numbers so, that the avarage of the left numbers is a whole number

(5u + 6)-(3u+2)=

A regional candy factory sells a guava roll at a price of $48, the monthly fixed costs amount to $125,000 and the variable cost for making a guava roll is $28. Determine: a) The equation of the total income from the production of guava rolls.

A company that manufactures personal hygiene items purchases machinery for $220,000 that is considered to last 7 years; it is estimated that at the end of the period it will have a salvage value of $1000. Find: to. The depreciation rate. b. The book value at the end of the sixth year.

A person borrows rm 1000 from a bank at an interest rate of 10%. After some time, he pays the bank rm 1900 as full and final settlement of the loan. Estimate the duration of his loan.

15/5+7-5

Raúl, Gilberto and Arturo are playing golf; The probabilities of winning for each one are as follows: (Raúl wins) = 20% (Gilberto wins) = 0.05% (Arturo wins) = ¾%. Perform operations and order events from least to most probable.

The price per night of a suite at the Baglioni Hotel in Venice is 1896 euros, VAT included. The VAT in Italy is 25%. The hotel gets a return of 10% out of the price VAT included. a) What is the amount of VAT paid by the hotel for one

Given (3x+2)E [2;14] how much money (in soles) does Sophia have if numerically it is the greatest value of x?

I. Order to add 40.25+1.31+.45 what is the first action to do ?

3/9*4/8=

Use linear approximation to estimate the value of the sine of 31o.

-1%2F2x-4%3D18

Find the minimum value of the function y = -4 x3 + 60 x2 -252 x + 8 for values of x between x = 0 and x = 9 Enter the value of the function, not the value of x

We have two distributions: A (M = 66.7, 95% CI = [60.3, 67.1]) / B (M = 71.3 95% CI = [67.7, 74.9]). Erin maintains that B is significantly larger than A. Provide your opinion on Erin’s argument and justify your opinion.

Consider the function f(x)=1/2(x+1)^2-3. Use the preceding/following interval method to estimate the instantaneous rate of change at 𝑥 = 1.

Question 3 A square has a perimeter given by the algebraic expression 24x – 16. Write the algebraic expression that represents one of its sides.

Multiply (2 + 3𝑖)(4 − 𝑖

Answer to a math question Multiply (2 + 3𝑖)(4 − 𝑖

You might be interested in