In Exercises 1–8, add or subtract as indicated and write the result in standard form. (7 + 2i) + (1 − 4i)

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Identify the problem as adding two complex numbers: \((7 + 2i)\) and \((1 - 4i)\).

Recall that to add complex numbers, you add their real parts together and their imaginary parts together separately.

Add the real parts: \(7 + 1\).

Add the imaginary parts: \(2i + (-4i)\).

Combine the results to write the sum in standard form \(a + bi\).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Complex Numbers and Their Standard Form

A complex number is expressed as a + bi, where a is the real part and b is the imaginary part. The standard form refers to writing complex numbers explicitly in this format, which helps in performing arithmetic operations clearly.

Addition and Subtraction of Complex Numbers

To add or subtract complex numbers, combine their real parts and their imaginary parts separately. For example, (a + bi) + (c + di) = (a + c) + (b + d)i, ensuring the result remains in standard form.

Imaginary Unit i and Its Properties

The imaginary unit i is defined by i² = -1. Understanding this property is essential when simplifying expressions involving complex numbers, especially when multiplying or combining terms with i.

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