Textbook Question
In Exercises 1–10, perform the indicated operations and write the result in standard form. (8 − 3i) − (17 − 7i)
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11. Graphing Complex Numbers
Graphing Complex Numbers
1:57 minutesProblem 3
Textbook Question
In Exercises 1–8, add or subtract as indicated and write the result in standard form. (3 + 2i) − (5 − 7i)
Verified step by step guidance1
Identify the problem as the subtraction of two complex numbers: \((3 + 2i) - (5 - 7i)\).
Recall that to subtract complex numbers, subtract their real parts and their imaginary parts separately.
Subtract the real parts: \$3 - 5$.
Subtract the imaginary parts: \$2i - (-7i)\(, which simplifies to \)2i + 7i$.
Combine the results to write the answer in standard form \(a + bi\), where \(a\) is the real part and \(b\) is the coefficient of \(i\).
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Video duration:
1mKey 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. The standard form means writing the result explicitly as a sum of a real number and an imaginary number.
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Complex Numbers In Polar Form
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.
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Imaginary Unit i and Its Properties
The imaginary unit i is defined as the square root of -1, with the property i² = -1. Understanding this helps in simplifying expressions involving imaginary parts.
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