Pure · Complex numbers
Chapter 1 · 3
The idea
Complex numbers in Cartesian form
The imaginary unit i with i² = −1, real and imaginary parts, equality of complex numbers, and the four operations in the form a + bi — addition, subtraction, multiplication, and division by realising the denominator with the conjugate.
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Pure · Complex numbers
Complex numbers in Cartesian form
The imaginary unit i with i² = −1, real and imaginary parts, equality of complex numbers, and the four operations in the form a + bi — addition, subtraction, multiplication, and division by realising the denominator with the conjugate.
Why it works
One new rule
A quadratic like has no real solution, because no real number squares to a negative. We extend the number system by defining a new symbol with Everything else follows from ordinary algebra with this one extra rule. A complex number is written , where and are real: is the real part and is the imaginary part (note the imaginary part is the real number , not ).Keep reading — free
The rest of the explanation, plus 3 worked examples you step through move by move.
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