5 Questions
What is the imaginary unit denoted as in complex numbers?
i
How can a complex number be expressed?
a - bi
Which polynomial equation has no real solution but has nonreal complex solutions?
(x + 1)^2 = -9
What is the real part of the complex number a + bi?
a
According to the fundamental theorem of algebra, what does every non-constant polynomial equation with real or complex coefficients have?
A solution which is a complex number
Study Notes
Complex Numbers
- The imaginary unit is denoted as i, where i = √(-1).
- A complex number can be expressed in standard form as a + bi, where a is the real part and bi is the imaginary part.
Polynomial Equations
- The quadratic equation x^2 + 1 = 0 has no real solution, but it has nonreal complex solutions.
Complex Number Properties
- The real part of the complex number a + bi is a.
Fundamental Theorem of Algebra
- According to the fundamental theorem of algebra, every non-constant polynomial equation with real or complex coefficients has at least one complex root (or solution).
Test your knowledge of complex numbers with this quiz. Explore the properties and expressions of complex numbers, including the role of the imaginary unit i.
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