Math Problem Statement

(3+i)−(7−i)

Solution

To solve the expression (3+i)(7i)(3 + i) - (7 - i), follow these steps:

  1. Distribute the negative sign: (3+i)(7i)=3+i7+i(3 + i) - (7 - i) = 3 + i - 7 + i

  2. Combine the real parts: 37=43 - 7 = -4

  3. Combine the imaginary parts: i+i=2ii + i = 2i

So, the simplified result is: 4+2i-4 + 2i

Would you like more details or further explanations?

Here are 5 related questions to explore:

  1. What are complex numbers and how are they used in mathematics?
  2. How do you multiply complex numbers?
  3. What is the complex conjugate of a number?
  4. How do you calculate the magnitude (or modulus) of a complex number?
  5. How do you add or subtract more than two complex numbers?

Tip: When dealing with complex numbers, always separate real and imaginary parts to simplify operations.

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Math Problem Analysis

Mathematical Concepts

Complex Numbers
Addition and Subtraction of Complex Numbers

Formulas

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

Theorems

Properties of Complex Numbers
Distributive Property

Suitable Grade Level

Grades 9-11