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

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Identify the problem as subtracting two complex numbers: \((-2 + 4i) - (-4 + 4i)\).

Rewrite the subtraction by distributing the negative sign to the second complex number: \((-2 + 4i) + (4 - 4i)\).

Group the real parts together and the imaginary parts together: \((-2 + 4) + (4i - 4i)\).

Simplify the real parts: \(-2 + 4\) and the imaginary parts: \(4i - 4i\) separately.

Write the final answer in standard form \(a + bi\) by combining the simplified real and imaginary parts.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Complex Numbers

Complex numbers are numbers in the form a + bi, where a is the real part and b is the imaginary part. The imaginary unit i satisfies i² = -1. Understanding this form is essential for performing operations like addition and subtraction.

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 process keeps the result in standard form.

Standard Form of a Complex Number

The standard form of a complex number is a + bi, where a and b are real numbers. Writing answers in this form clearly separates the real and imaginary parts, making it easier to interpret and use the result.

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