In Exercises 1–8, add or subtract as indicated and write the result in standard form. 8i − (14 − 9i)

검증된 단계별 안내

Identify the expression to simplify: $8i - (14 - 9i)$.

Distribute the negative sign across the terms inside the parentheses: $8i - 14 + 9i$.

Group the real parts and the imaginary parts separately: $(-14) + (8i + 9i)$.

Combine like terms: the real part remains $-14$, and the imaginary parts add up to \$17i$.

Write the final expression in standard form $a + bi$: $-14 + 17i$.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

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주요 개념

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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. The standard form ensures clarity in addition, subtraction, and other operations by separating real and imaginary components.

Addition and Subtraction of Complex Numbers

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

Distributive Property in Algebra

The distributive property allows you to remove parentheses by multiplying a term outside the parentheses by each term inside. For example, a(b - c) = ab - ac, which is essential when subtracting complex numbers with parentheses.