https://file.aiquickdraw.com/mathbot/file/1729809037986lex610zv.jpg

I see the math problems in your image involve complex numbers. Let me solve a few of them for you step by step. I'll start with the first four problems in the image:

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**11.** \((-4 - 7i) - (4 + 5i) - (2 - i)\)

1. First, distribute the negative signs:
   \[ = -4 - 7i - 4 - 5i - 2 + i \]
2. Combine like terms (real and imaginary):
   \[ = (-4 - 4 - 2) + (-7i - 5i + i) \]
   \[ = -10 - 11i \]
   
So, the answer is **\(-10 - 11i\)**.

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**12.** \((-1 + i) - (-7 + 4i) - 5\)

1. Distribute the negative signs:
   \[ = -1 + i + 7 - 4i - 5 \]
2. Combine like terms:
   \[ = (-1 + 7 - 5) + (i - 4i) \]
   \[ = 1 - 3i \]

So, the answer is **\(1 - 3i\)**.

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**13.** \((-1 + 6i) + (5 - 2i) - (8i)\)

1. Combine like terms (real and imaginary):
   \[ = (-1 + 5) + (6i - 2i - 8i) \]
   \[ = 4 - 4i \]

So, the answer is **\(4 - 4i\)**.

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**14.** \((1 + 6i) + (6 - 2i) - (-7 + 5i)\)

1. Distribute the negative sign:
   \[ = 1 + 6i + 6 - 2i + 7 - 5i \]
2. Combine like terms:
   \[ = (1 + 6 + 7) + (6i - 2i - 5i) \]
   \[ = 14 - i \]

So, the answer is **\(14 - i\)**.

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Would you like details on any of these steps? Feel free to ask, and I can also continue solving the rest of the problems.

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Here are five related questions for practice:
1. How do you simplify the addition and subtraction of complex numbers?
2. What is the result of \((3 + 2i) + (4 - i)\)?
3. What is the conjugate of the complex number \(5 - 7i\)?
4. Can complex numbers be ordered like real numbers? Why or why not?
5. How do you visualize complex numbers on the complex plane?

**Tip:** Always separate the real and imaginary parts when adding or subtracting complex numbers.

Learn how to simplify the expression (-4 - 7i) - (4 + 5i) - (2 - i) by distributing negative signs and combining like terms. This problem focuses on the addition and subtraction of complex numbers, suitable for Grade 10-12 students.

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