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

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First, rewrite the expression clearly: \((-4 - i) - (2 + 3i) + (-4 + 5i)\).

Next, distribute the subtraction sign to the second group: \((-4 - i) - 2 - 3i + (-4 + 5i)\).

Now, group the real parts together and the imaginary parts together: \((-4 - 2 - 4) + (-i - 3i + 5i)\).

Combine the real parts: \(-4 - 2 - 4\) and combine the imaginary parts: \(-1i - 3i + 5i\).

Write the final answer in standard form \(a + bi\) by putting the combined real part and imaginary part together.

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Key Concepts

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

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 imaginary unit i as a variable, ensuring the real and imaginary components are handled independently.

Distributive Property and Grouping Like Terms

When dealing with sums and differences of complex numbers, use the distributive property to remove parentheses and then group like terms (real with real, imaginary with imaginary) to simplify the expression efficiently.

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