Math Problem Statement

Evaluate the expression (6 - 2i) - (-4 - i) and write the result in the form a + bi.

Solution

Let's evaluate the expression (62i)(4i)(6 - 2i) - (-4 - i).

We will handle this by subtracting the real and imaginary parts separately:

  1. Real part: 6(4)=6+4=106 - (-4) = 6 + 4 = 10
  2. Imaginary part: 2i(i)=2i+i=i-2i - (-i) = -2i + i = -i

So, the result is:

(62i)(4i)=10i(6 - 2i) - (-4 - i) = 10 - i

Thus, in the form a+bia + bi, we have:

  • a=10a = 10
  • b=1b = -1

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

Here are 5 related questions you might consider:

  1. How do you add or subtract complex numbers in general?
  2. What is the geometric interpretation of complex numbers on the complex plane?
  3. How do you multiply two complex numbers?
  4. What is the modulus of a complex number?
  5. How can you convert a complex number from rectangular to polar form?

Tip: When subtracting complex numbers, treat the real and imaginary parts separately, just like combining like terms in algebra.

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Math Problem Analysis

Mathematical Concepts

Complex Numbers
Subtraction of Complex Numbers

Formulas

(a + bi) - (c + di) = (a - c) + (b - d)i

Theorems

Arithmetic of Complex Numbers

Suitable Grade Level

Grades 9-12