Perform each operation. Write answers in standard form. (6-i) + (7-2i)

Verified step by step guidance

1. Identify the problem as the addition of two complex numbers: \((6 - i)\) and \((7 - 2i)\).
2. Recall that to add complex numbers, you add their real parts together and their imaginary parts together separately.
3. Add the real parts: \(6 + 7\).
4. Add the imaginary parts: \(-i + (-2i)\), which is the same as \(-1i - 2i\).
5. Combine the sums of the real and imaginary parts to write the result in standard form: \(a + bi\).

Key Concepts

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 real and imaginary parts, allowing operations beyond the real number system.

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 simplify.

Standard Form of Complex Numbers

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