Math Problem Statement

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

Solution

Let's multiply the complex numbers (26i)(-2 - 6i) and (3+i)(3 + i).

We will apply the distributive property (also known as the FOIL method for binomials):

(26i)(3+i)=(2)(3)+(2)(i)+(6i)(3)+(6i)(i)(-2 - 6i)(3 + i) = (-2)(3) + (-2)(i) + (-6i)(3) + (-6i)(i)

Now, calculate each term:

  1. (2)(3)=6(-2)(3) = -6
  2. (2)(i)=2i(-2)(i) = -2i
  3. (6i)(3)=18i(-6i)(3) = -18i
  4. (6i)(i)=6i2(-6i)(i) = -6i^2 (Remember that i2=1i^2 = -1, so this becomes 66)

Now, combine all the terms:

62i18i+6=(66)+(2i18i)=020i-6 - 2i - 18i + 6 = (6 - 6) + (-2i - 18i) = 0 - 20i

Thus, the product of (26i)(3+i)(-2 - 6i)(3 + i) is:

20i-20i

If you'd like more details or have any questions, feel free to ask!


Here are 5 related questions for you to explore:

  1. What happens if we multiply a complex number by its conjugate?
  2. How do we divide complex numbers?
  3. Can complex numbers be added or subtracted directly? If so, how?
  4. What is the modulus of a complex number, and how do you calculate it?
  5. How do you express a complex number in polar form?

Tip: When multiplying complex numbers, remember to distribute each term and simplify carefully, especially when dealing with powers of ii.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Complex Numbers
Multiplication of Complex Numbers
Algebra

Formulas

Distributive Property (FOIL method)
i^2 = -1

Theorems

Multiplying Complex Numbers

Suitable Grade Level

Grades 9-11