Questions: Perform the indicated operation and express the result as a simplified complex number. (-4+4 i)-(-7+8 i)

Perform the indicated operation and express the result as a simplified complex number. (-4+4 i)-(-7+8 i)
Transcript text: Perform the indicated operation and express the result as a simplified complex number. \[ (-4+4 i)-(-7+8 i) \]
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Solution

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Solution Steps

To solve the given problem, we need to perform the subtraction of two complex numbers. We will subtract the real parts and the imaginary parts separately.

Step 1: Define the Complex Numbers

We start with the given complex numbers: \[ z_1 = -4 + 4i \] \[ z_2 = -7 + 8i \]

Step 2: Subtract the Complex Numbers

To subtract \(z_2\) from \(z_1\), we subtract the real parts and the imaginary parts separately: \[ (-4 + 4i) - (-7 + 8i) \]

Step 3: Simplify the Real and Imaginary Parts

First, simplify the real parts: \[ -4 - (-7) = -4 + 7 = 3 \]

Next, simplify the imaginary parts: \[ 4i - 8i = -4i \]

Final Answer

Combining the simplified real and imaginary parts, we get: \[ 3 - 4i \]

\(\boxed{3 - 4i}\)

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