Math Problem Statement

Simplify (-4i)(-6-2i)

Solution

To simplify the expression (4i)(62i)(-4i)(-6 - 2i), we can follow these steps:

  1. Distribute the 4i-4i to both terms in the parentheses: (4i)(6)+(4i)(2i)(-4i)(-6) + (-4i)(-2i)

  2. Multiply each term:

    • (4i)(6)=24i(-4i)(-6) = 24i
    • (4i)(2i)=8i2(-4i)(-2i) = 8i^2
  3. Recall that i2=1i^2 = -1, so: 8i2=8(1)=88i^2 = 8(-1) = -8

  4. Now, combine the results: 24i824i - 8

So, the simplified expression is: 8+24i-8 + 24i

Would you like further explanation or have any questions about this solution?

Here are some related questions you can explore:

  1. How does multiplying complex numbers work in general?
  2. What is the conjugate of a complex number, and how do you use it?
  3. What is the modulus of a complex number, and how is it calculated?
  4. How can you express complex numbers in polar form?
  5. What is the difference between real and imaginary parts of a complex number?

Tip: When multiplying complex numbers, always remember to apply the distributive property and replace i2i^2 with 1-1.

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Math Problem Analysis

Mathematical Concepts

Complex Numbers
Multiplying Complex Numbers

Formulas

i^2 = -1

Theorems

Distributive Property

Suitable Grade Level

Grades 9-11