Question

question 25
for the following exercise, perform the indicated operations and express the result as a simplified complex number.
(1 - 5i) + (-5 + i) =
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question 26
for the following exercise, perform the indicated operations and express the result as a simplified complex number.
(4 - 3i) - (-1 + 3i) =
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Explanation:

Question 25

Step1: Combine real parts

Real parts: \(1 + (-5) = 1 - 5 = -4\)

Step2: Combine imaginary parts

Imaginary parts: \(-5i + i = (-5 + 1)i = -4i\)

Step3: Combine results

\((1 - 5i) + (-5 + i) = -4 - 4i\)

Step1: Distribute the negative sign

\((4 - 3i) - (-1 + 3i) = 4 - 3i + 1 - 3i\)

Step2: Combine real parts

Real parts: \(4 + 1 = 5\)

Step3: Combine imaginary parts

Imaginary parts: \(-3i - 3i = (-3 - 3)i = -6i\)

Step4: Combine results

\(4 - 3i + 1 - 3i = 5 - 6i\)

Answer:

\(-4 - 4i\)

Question 26