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

Verified step by step guidance

1. Identify the given 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: \(-i + (-2i)\).
5. Combine the sums 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 and are used to represent quantities that cannot be expressed on the real number line alone.

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. This operation follows the standard algebraic rules applied to the components.

Standard Form of a Complex Number

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 standard form means expressing the result clearly with real and imaginary parts separated.