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Course: Algebra 2 > Unit 2
Lesson 6: Quadratic equations with complex solutionsComplex numbers: FAQ
Frequently asked questions about complex numbers
What is the imaginary unit ?
The imaginary unit is a special number that, when squared, gives us . It's a key part of complex numbers, which we'll learn about in this unit.
What are complex numbers?
Complex numbers are numbers that have both a "real" part and an "imaginary" part. We can write them as , where is the real part and is the imaginary part.
What are some real-world applications of complex numbers?
Complex numbers are used in a wide variety of fields, such as engineering, physics, and mathematics. They are especially useful for modeling certain types of electrical circuits and for analyzing signals in electronics.
What is the complex plane?
The complex plane is a way of visualizing complex numbers. We plot the real part of the number on the horizontal axis, and the imaginary part on the vertical axis.
How do we add and subtract complex numbers?
To add or subtract two complex numbers, we combine their real parts and their imaginary parts separately. For example, .
How do we multiply complex numbers?
To multiply two complex numbers, we use the distributive property to multiply all the terms together. For example:
Why do we need complex numbers to solve some quadratic equations?
Some quadratic equations don't have any "real" solutions, but they do have complex solutions. For example, doesn't have any real solutions, but it does have the two complex solutions .
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