Find each sum or difference. Write answers in standard form. (2-5i) - (3+4i) - (-2+i)

Verified step by step guidance

1. Identify the problem as subtracting complex numbers and writing the result in standard form, which is \(a + bi\) where \(a\) and \(b\) are real numbers.
2. Rewrite the expression by removing parentheses carefully, remembering to distribute the minus signs: \((2 - 5i) - (3 + 4i) - (-2 + i)\) becomes \(2 - 5i - 3 - 4i + 2 - i\).
3. Group the real parts together and the imaginary parts together: \((2 - 3 + 2) + (-5i - 4i - i)\).
4. Simplify the real parts by performing the addition and subtraction: \(2 - 3 + 2\).
5. Simplify the imaginary parts by combining like terms: \(-5i - 4i - i\), then write the final answer in the 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. Writing answers in standard form means presenting the result explicitly as a sum of a real number and an imaginary number.

Addition and Subtraction of Complex Numbers

To add or subtract complex numbers, combine their real parts separately and their imaginary parts separately. This process treats the real and imaginary components like like terms in algebra.

Distributive Property and Handling Negative Signs

When subtracting complex numbers, apply the distributive property to remove parentheses, especially when a negative sign precedes a parenthesis. This ensures correct sign changes for both real and imaginary parts.