Question

subtract.
(2 - i) - (6 - 2i)
write your answer as a complex number in standard form.

Explanation:

Step1: Distribute the negative sign

To subtract the complex numbers, we first distribute the negative sign to the second complex number:
\((2 - i) - (6 - 2i) = 2 - i - 6 + 2i\)

Step2: Combine the real parts and the imaginary parts

Next, we combine the real parts (\(2\) and \(-6\)) and the imaginary parts (\(-i\) and \(2i\)) separately:
Real parts: \(2 - 6 = -4\)
Imaginary parts: \(-i + 2i = i\)

Step3: Write in standard form

The standard form of a complex number is \(a + bi\), where \(a\) is the real part and \(b\) is the coefficient of the imaginary part. Combining the results from Step 2, we get:
\(-4 + i\)

Answer:

\(-4 + i\)