In Exercises 1–10, perform the indicated operations and write the result in standard form. (8 − 3i) − (17 − 7i)

Verified step by step guidance

1. Identify the problem as a subtraction of two complex numbers: \((8 - 3i) - (17 - 7i)\).
2. Recall that to subtract complex numbers, subtract their real parts and their imaginary parts separately.
3. Subtract the real parts: \$8 - 17$.
4. Subtract the imaginary parts: \(-3i - (-7i)\), which simplifies to \(-3i + 7i\).
5. Combine the results from the real and imaginary parts to write the answer in standard form \(a + bi\).

Key Concepts

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 refers to writing the result explicitly as a sum of a real number and an imaginary number, making it easier to interpret and use in further calculations.

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) equals (a - c) + (b - d)i. This operation follows the same rules as combining like terms in algebra.

Imaginary Unit Properties

The imaginary unit i is defined such that i² = -1. Understanding this property is essential when simplifying expressions involving complex numbers, especially when multiplying or dividing, though it is less directly involved in simple addition or subtraction.