Answered

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3. Simplify the expression:

[tex]\[ (2 - 5i) - (4 - 4i) \][/tex]

A. [tex]\( 2 + i \)[/tex]
B. [tex]\(-3i \)[/tex]
C. [tex]\(-2 - i \)[/tex]
D. [tex]\(6 - 9i \)[/tex]

Sagot :

GinnyAnswer
To simplify the expression [tex]\((2 - 5i) - (4 - 4i)\)[/tex], follow these steps:

1. Distribute the subtraction across the complex numbers:
[tex]\[ (2 - 5i) - (4 - 4i) = 2 - 5i - 4 + 4i \][/tex]

2. Combine the real parts:
[tex]\[ 2 - 4 = -2 \][/tex]

3. Combine the imaginary parts:
[tex]\[ -5i + 4i = -i \][/tex]

Putting it all together:
[tex]\[ (2 - 5i) - (4 - 4i) = -2 - i \][/tex]

Therefore, the simplified expression is [tex]\( \boxed{-2 - i} \)[/tex].

Given the provided options:
- [tex]\(2 + i\)[/tex]
- [tex]\(-3i\)[/tex]
- [tex]\(-2 - i\)[/tex]
- [tex]\(6 - 9i\)[/tex]

The correct choice is:
[tex]\( \boxed{-2 - i} \)[/tex]
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