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

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

2. Combine the real parts \((-10) - (2)\):
   \[
   -10 - 2 = -12
   \]

3. Combine the imaginary parts \((-3i) - (10i)\):
   \[
   -3i - 10i = -13i
   \]

4. The final expression is:
   \[
   -12 - 13i
   \]

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

Would you like further details or have any questions?

Here are 5 related questions for practice:
1. What is the result of \((4 + 5i) + (3 - 2i)\)?
2. How do you multiply two complex numbers like \((2 + i)(1 - 3i)\)?
3. What is the conjugate of the complex number \(-12 - 13i\)?
4. How do you find the magnitude of the complex number \(3 + 4i\)?
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.

Learn how to subtract the complex numbers (−10−3i) and (2+10i) with a detailed, step-by-step solution. This problem explains how to combine real and imaginary parts, showcasing key concepts in complex number arithmetic. Suitable for students in Grades 10-12.

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