Math Problem Statement

(−10−3i)−(2+10i)

Solution

Let's break down the expression (103i)(2+10i)(−10−3i)−(2+10i).

  1. Distribute the minus sign to both terms in the second set of parentheses: (103i)(2+10i)=103i210i(-10 - 3i) - (2 + 10i) = -10 - 3i - 2 - 10i

  2. Combine the real parts (10)(2)(-10) - (2): 102=12-10 - 2 = -12

  3. Combine the imaginary parts (3i)(10i)(-3i) - (10i): 3i10i=13i-3i - 10i = -13i

  4. The final expression is: 1213i-12 - 13i

Thus, the result of (103i)(2+10i)(−10−3i)−(2+10i) is 1213i-12 - 13i.

Would you like further details or have any questions?

Here are 5 related questions for practice:

  1. What is the result of (4+5i)+(32i)(4 + 5i) + (3 - 2i)?
  2. How do you multiply two complex numbers like (2+i)(13i)(2 + i)(1 - 3i)?
  3. What is the conjugate of the complex number 1213i-12 - 13i?
  4. How do you find the magnitude of the complex number 3+4i3 + 4i?
  5. How do you represent complex numbers in polar form?

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

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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

Basic properties of complex numbers

Suitable Grade Level

Grades 10-12