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

검증된 단계별 안내

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 \(a + bi\).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.