Summary: Linear Algebra Foe
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3 1.2 Complex Numbers
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How is the solution of Equation (1) expressed using complex numbers?
- Solution is expressed as x ± i
- Example: 4 ± i, 3 ± 3i
- Complex numbers include real and imaginary parts -
What makes it possible to find the solution of any quadratic equation of a certain form?
- Existence of square root of a negative number
- Solvable using complex numbers
- Quadratic equation of the form ax^2 + bx + c -
How are complex numbers represented in the form of a + bi?
- Denoted as a + bi
- a and b are real numbers
- i = sqrt(-1) -
What letter is generally used to denote a complex number?
- Complex numbers are denoted by the letter Z
- Expressed as z = a + bi
- a, b are real numbers and i = sqrt(-1) -
What property does the "new number" i have in the solution of Equation (1)?
- Property: i = sqrt(-1)
- Enables the solution of Equations with no real roots
- Forms complex numbers when combined with real numbers -
What is the real part of a complex number generally denoted as?
- Re(z) -
How is the imaginary part of a complex number generally denoted as?
- Im(z) -
What is the real part of the complex number z = a + bi?
- a -
What does the letter z often represent in complex numbers?
- A complex number -
What is a complex number called if it is equal to zero?
- A purely imaginary number
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