Math Problem Statement

(10+15i)-(48-30i)

Solution

To simplify the expression (10+15i)(4830i)(10 + 15i) - (48 - 30i), follow these steps:

Step 1: Distribute the negative sign

The expression becomes: 10+15i48+30i10 + 15i - 48 + 30i

Step 2: Combine the real parts and imaginary parts

  • Real part: 1048=3810 - 48 = -38
  • Imaginary part: 15i+30i=45i15i + 30i = 45i

Final result:

38+45i-38 + 45i

So, the simplified result is 38+45i-38 + 45i.

Would you like further clarification or more examples?

Here are 5 related questions to explore further:

  1. How do you simplify expressions involving complex conjugates?
  2. What is the geometric interpretation of complex numbers?
  3. How do you multiply complex numbers?
  4. What is the modulus of a complex number?
  5. How do you divide complex numbers?

Tip: When adding or subtracting complex numbers, always separate the real and imaginary parts and combine them separately!

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Math Problem Analysis

Mathematical Concepts

Complex Numbers
Algebra

Formulas

Addition and Subtraction of Complex Numbers: (a+bi) ± (c+di) = (a±c) + (b±d)i

Theorems

Properties of Complex Numbers

Suitable Grade Level

Grades 9-10