In Exercises 1–8, add or subtract as indicated and write the result in standard form. 6 − (−5 + 4i) − (−13 − i)

검증된 단계별 안내

Identify the expression to simplify: \(6 - (-5 + 4i) - (-13 - i)\).

Apply the distributive property to remove the parentheses by changing the signs inside each parenthesis preceded by a minus: \(6 + 5 - 4i + 13 + i\).

Group the real parts together and the imaginary parts together: \((6 + 5 + 13) + (-4i + i)\).

Add the real parts: \(6 + 5 + 13\), and add the imaginary parts: \(-4i + i\) separately.

Write the final expression in standard form \(a + bi\), where \(a\) is the sum of the real parts and \(b\) is the sum of the imaginary parts.

비슷한 문제에 대한 검증된 영상 답변:

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주요 개념

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

Complex Numbers and Standard Form

Complex numbers are expressed in the form a + bi, where a is the real part and b is the imaginary part. Writing a complex number in standard form means presenting it clearly as a sum or difference of its real and imaginary components.

Addition and Subtraction of Complex Numbers

To add or subtract complex numbers, combine their real parts separately and their imaginary parts separately. This process is similar to combining like terms in algebra, ensuring the result remains in standard form.

Handling Negative Signs and Parentheses

When subtracting complex numbers, carefully distribute the negative sign across all terms inside the parentheses. This step is crucial to avoid sign errors and correctly simplify the expression.