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Questions and Answers
What is the solution to the equation $x^2 + 1 = 0$?
What is the solution to the equation $x^2 + 1 = 0$?
How is a complex number defined?
How is a complex number defined?
What is the real part of the complex number $z = 3 + 2i$?
What is the real part of the complex number $z = 3 + 2i$?
What is the imaginary part of the complex number $w = 5 - 4i$?
What is the imaginary part of the complex number $w = 5 - 4i$?
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When are two complex numbers equal?
When are two complex numbers equal?
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Study Notes
Solutions to Complex Equations
- The equation ( x^2 + 1 = 0 ) has solutions that can be found by rearranging to ( x^2 = -1 ).
- Solutions to the equation are ( x = i ) and ( x = -i ), where ( i ) is the imaginary unit defined by ( i^2 = -1 ).
Definition of Complex Numbers
- A complex number is defined as a number of the form ( z = a + bi ), where:
- ( a ) is the real part.
- ( b ) is the imaginary part.
- ( i ) is the imaginary unit.
Real and Imaginary Parts
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For the complex number ( z = 3 + 2i ):
- The real part is ( 3 ).
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For the complex number ( w = 5 - 4i ):
- The imaginary part is ( -4 ).
Conditions for Equality of Complex Numbers
- Two complex numbers ( z_1 = a + bi ) and ( z_2 = c + di ) are equal if and only if:
- Their real parts are equal: ( a = c ).
- Their imaginary parts are equal: ( b = d ).
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Description
Test your knowledge of complex numbers and quadratic equations with this quiz on Chapter 4 of Mathematics. Dive into the realm of imaginary numbers and explore the solutions to quadratic equations.
