Questions: (-10+2i)+(-10i-2)

Transcript text: $(-10+2 \imath)+(-10 \imath-2)$

Solution

Solution Steps

To solve the given expression, we need to perform addition of complex numbers. Complex numbers are added by separately adding their real parts and their imaginary parts.

Solution Approach

Identify the real and imaginary parts of each complex number.
Add the real parts together.
Add the imaginary parts together.
Combine the results to form the final complex number.

Step 1: Identify the Complex Numbers

Given the complex numbers: \[ z_1 = -10 + 2i \] \[ z_2 = -2 - 10i \]

Step 2: Add the Real Parts

Add the real parts of $ z_1 $ and $ z_2 $: \[ \text{Real part} = -10 + (-2) = -12 \]

Step 3: Add the Imaginary Parts

Add the imaginary parts of $ z_1 $ and $ z_2 $: \[ \text{Imaginary part} = 2 + (-10) = -8 \]

Step 4: Combine the Results

Combine the real and imaginary parts to form the final complex number: \[ z = -12 - 8i \]

Final Answer

$\boxed{-12 - 8i}$

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