Questions: Find the difference of the following expressions. [ (-5-8 i)-(7-6 i) ]

Find the difference of the following expressions. [ (-5-8 i)-(7-6 i) ]
Transcript text: Find the difference of the following expressions. \[ (-5-8 i)-(7-6 i) \] Answer
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Solution

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Solution Steps

Step 1: Define the Complex Numbers

We start by defining the complex numbers involved in the expression: \[ z_1 = -5 - 8i \] \[ z_2 = 7 - 6i \]

Step 2: Set Up the Expression

Next, we set up the expression for the difference of the two complex numbers: \[ z_1 - z_2 = (-5 - 8i) - (7 - 6i) \]

Step 3: Perform the Subtraction

Now, we perform the subtraction by combining the real and imaginary parts: \[ (-5 - 8i) - (7 - 6i) = (-5 - 7) + (-8 + 6)i = -12 - 2i \]

Step 4: State the Result

The result of the difference of the expressions is: \[ -12 - 2i \]

Final Answer

\(\boxed{-12 - 2i}\)

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