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What is the standard form of this complex number?

[tex](24-10i)-(43+18i)[/tex]

A. [tex]-19-28i[/tex]
B. [tex]67+28i[/tex]
C. [tex]-19+18i[/tex]
D. [tex]-19+8i[/tex]


Sagot :

To solve the problem of subtracting the complex numbers [tex]\( (24 - 10i) - (43 + 18i) \)[/tex], let's break the problem into smaller, more manageable steps.

1. Identify the Real and Imaginary Parts:
- The first complex number [tex]\( 24 - 10i \)[/tex]:
- Real part: 24
- Imaginary part: -10
- The second complex number [tex]\( 43 + 18i \)[/tex]:
- Real part: 43
- Imaginary part: 18

2. Subtract the Real Parts:
[tex]\[ 24 - 43 = -19 \][/tex]

3. Subtract the Imaginary Parts:
[tex]\[ -10 - 18 = -28 \][/tex]

4. Combine the Results:
- The real part of the result: [tex]\( -19 \)[/tex]
- The imaginary part of the result: [tex]\( -28 \)[/tex]
- Therefore, the result of the subtraction is:
[tex]\[ -19 - 28i \][/tex]

5. Match the Result with the Given Options:
- Option A: [tex]\( -19 - 28i \)[/tex]
- Option B: [tex]\( 67 + 28i \)[/tex]
- Option C: [tex]\( -19 + 18i \)[/tex]
- Option D: [tex]\( -19 + 8i \)[/tex]

6. Select the Correct Option:
- Comparing the result [tex]\( -19 - 28i \)[/tex] with the options provided, we find that it matches Option A.

Therefore, the standard form of the complex number after the subtraction is:
[tex]\[ \boxed{-19 - 28i} \][/tex]