Arithmetic operations on complex numbers Amount The sum of the complex numbers z1 = a + bi and z2 = c + di is the complex number (a + c) + (b + d) i.
In this way:
z1 + z2 = (a + bi) + (c + di) = (a + c) + (b + d) i.
The sum of complex numbers has the properties:
- commutativity: z1 + z2 = z2 + z1
- associativity: (z1 + z2) + z3 = z1 + (z2 + z3)
Composition
The product of the complex numbers z1 = a + bi and z2 = c + di is the complex number (ac - bd) + (ad + bc) i. The definition of a work is established in such a way that (a + bi) and (c + di) can be multiplied as algebraic binomials, assuming that i * i = -1.
The product of complex numbers has the properties: - commutativity: z1 * z2 = z2 * z1
- associativity: (z1 * z2) * z3 = z1 * (z2 * z3)
- distributivity: z1 * (z2 + z3) = z1 * z2 + z1 * z3
Based on the definition of the product of complex numbers, it is possible to determine the natural degree of a complex number : z (to the power n); = z * z * ... * zn times.
Difference
The difference of the complex numbers z1 = a + bi and z2 = c + di is the complex number z = z1 - z2 = (a - c) + (b - d) i.
Private
Particular from dividing the complex number z1 by the complex number z2 is such a number z that satisfies the condition z? z2 = z2? z = z1.
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