Math Problem Statement

(3 - 5i) - (-1 + 8i)

Solution

To simplify the given expression (35i)(1+8i)(3 - 5i) - (-1 + 8i), follow these steps:

  1. Distribute the negative sign across the second complex number: (35i)(1+8i)=(35i)+(18i)(3 - 5i) - (-1 + 8i) = (3 - 5i) + (1 - 8i)

  2. Combine the real parts and the imaginary parts:

    • Real parts: 3+1=43 + 1 = 4
    • Imaginary parts: 5i8i=13i-5i - 8i = -13i

Thus, the simplified expression is: 413i4 - 13i

So, the values for the placeholders are:

  • Real part: 44
  • Imaginary part: 13-13

Would you like further details on how this works or any clarifications?

Here are 5 related questions you might find helpful:

  1. How do you add and subtract complex numbers?
  2. What are the real and imaginary parts of a complex number?
  3. Can complex numbers be represented graphically?
  4. How do you multiply complex numbers?
  5. What is the geometric interpretation of adding complex numbers?

Tip: Always group real and imaginary parts separately when simplifying complex expressions.

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Math Problem Analysis

Mathematical Concepts

Complex Numbers
Algebra

Formulas

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

Theorems

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Suitable Grade Level

Grades 9-11