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Questions and Answers
What is the imaginary unit denoted as in complex numbers?
What is the imaginary unit denoted as in complex numbers?
- i (correct)
- l
- k
- j
Which part of the complex number a + bi is called the imaginary part?
Which part of the complex number a + bi is called the imaginary part?
- i
- b (correct)
- bi
- a
What does the fundamental theorem of algebra assert about non-constant polynomial equations?
What does the fundamental theorem of algebra assert about non-constant polynomial equations?
- They have a complex number solution (correct)
- They have only imaginary solutions
- They only have real solutions
- They have no solutions
How are complex numbers regarded in the mathematical sciences?
How are complex numbers regarded in the mathematical sciences?
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Why can't the equation (x + 1)^2 = -9 have a real solution?
Why can't the equation (x + 1)^2 = -9 have a real solution?
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Study Notes
Complex Numbers
- The imaginary unit is denoted as
iin complex numbers.
Structure of Complex Numbers
- The imaginary part of a complex number
a + biisbi.
Fundamental Theorem of Algebra
- The fundamental theorem of algebra asserts that every non-constant polynomial equation has at least one complex solution.
Significance of Complex Numbers
- Complex numbers are regarded as a fundamental tool in the mathematical sciences.
Solving Quadratic Equations
- The equation
(x + 1)^2 = -9cannot have a real solution because the square of any real number is non-negative.
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