Find each sum or difference. Write answers in standard form. (3+2i) + (9+3i)

검증된 단계별 안내

Identify the problem as adding two complex numbers: \((3 + 2i)\) and \((9 + 3i)\).

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

Add the real parts: \(3 + 9\).

Add the imaginary parts: \(2i + 3i\).

Write the result in standard form as the sum of the real part and the imaginary part: \((\text{real part}) + (\text{imaginary part})i\).

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주요 개념

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Complex Numbers

Complex numbers are numbers in the form a + bi, where a and b are real numbers and i is the imaginary unit with the property i² = -1. They combine a real part and an imaginary part, allowing for operations beyond the real number line.

Addition of Complex Numbers

To add complex numbers, add their real parts together and their imaginary parts together separately. For example, (a + bi) + (c + di) = (a + c) + (b + d)i, combining like terms to form a new complex number.

Standard Form of Complex Numbers

The standard form of a complex number is written as a + bi, where a is the real part and b is the coefficient of the imaginary part. Writing answers in this form clearly separates the real and imaginary components.