Math Problem Statement

(-4 - 7i) - (4 + 5i) - (2 - i)

Solution

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:


11. (47i)(4+5i)(2i)(-4 - 7i) - (4 + 5i) - (2 - i)

  1. First, distribute the negative signs: =47i45i2+i= -4 - 7i - 4 - 5i - 2 + i
  2. Combine like terms (real and imaginary): =(442)+(7i5i+i)= (-4 - 4 - 2) + (-7i - 5i + i) =1011i= -10 - 11i

So, the answer is 1011i-10 - 11i.


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

  1. Distribute the negative signs: =1+i+74i5= -1 + i + 7 - 4i - 5
  2. Combine like terms: =(1+75)+(i4i)= (-1 + 7 - 5) + (i - 4i) =13i= 1 - 3i

So, the answer is 13i1 - 3i.


13. (1+6i)+(52i)(8i)(-1 + 6i) + (5 - 2i) - (8i)

  1. Combine like terms (real and imaginary): =(1+5)+(6i2i8i)= (-1 + 5) + (6i - 2i - 8i) =44i= 4 - 4i

So, the answer is 44i4 - 4i.


14. (1+6i)+(62i)(7+5i)(1 + 6i) + (6 - 2i) - (-7 + 5i)

  1. Distribute the negative sign: =1+6i+62i+75i= 1 + 6i + 6 - 2i + 7 - 5i
  2. Combine like terms: =(1+6+7)+(6i2i5i)= (1 + 6 + 7) + (6i - 2i - 5i) =14i= 14 - i

So, the answer is 14i14 - i.


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


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)+(4i)(3 + 2i) + (4 - i)?
  3. What is the conjugate of the complex number 57i5 - 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.

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Math Problem Analysis

Mathematical Concepts

Complex Numbers
Algebra

Formulas

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

Theorems

Properties of Complex Number Addition and Subtraction

Suitable Grade Level

Grade 10-12