Textbook Question
In Exercises 21–28, divide and express the result in standard form. 8i / 4−3i
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11. Graphing Complex Numbers
Graphing Complex Numbers
1:33 minutesProblem 1
Textbook Question
In Exercises 1–8, add or subtract as indicated and write the result in standard form. (7 + 2i) + (1 − 4i)
Verified step by step guidance1
Identify the problem as adding two complex numbers: \((7 + 2i)\) and \((1 - 4i)\).
Recall that to add complex numbers, you add their real parts together and their imaginary parts together separately.
Add the real parts: \$7 + 1$.
Add the imaginary parts: \$2i + (-4i)$.
Combine the results to write the sum in standard form \(a + bi\).
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1mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Complex Numbers and Their Standard Form
A complex number is expressed as a + bi, where a is the real part and b is the imaginary part. The standard form refers to writing complex numbers explicitly in this format, which helps in performing arithmetic operations clearly.
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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, ensuring the result remains in standard form.
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Imaginary Unit i and Its Properties
The imaginary unit i is defined by i² = -1. Understanding this property is essential when simplifying expressions involving complex numbers, especially when multiplying or combining terms with i.
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