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They were discovered when Cardano solved the third degree equation.
In the formulas that arose to solve the third degree equation, Cardano needed to take the square root of negative numbers and add them up in a certain way. The strange thing that happened was that the formulas used these complex numbers, even if the solutions to the equation where all real. This baffled the mathematicians of the time, because how could these strange numbers turn out to be "real"?
Later this was considered totally correct, when the field of complex numbers was better undestood.
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∙ 11y ago
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What is complex math?
Complex math covers how to do operations on complex numbers. Complex numbers include real numbers, imaginary numbers, and the combination of real+imaginary numbers.
Are complex numbers under addition and multiplication a field?
The complex numbers are a field.
Which of these are complex numbers 5 3i 1 2i?
All of them. Real numbers are a subset of complex numbers.
What mathematician introduced complex numbers?
Gerolamo Cardano is an Italian mathematician who introduced complex numbers. Complex numbers are those that can be expressed in the form of a+bi where a and b represent real numbers.
Is -7 a complex number?
Yes, all real numbers are complex numbers.
What is complex math?
Complex math covers how to do operations on complex numbers. Complex numbers include real numbers, imaginary numbers, and the combination of real+imaginary numbers.
What is the relation of complex numbers to real numbers?
Complex numbers are a proper superset of real numbers. That is to say, real numbers are a proper subset of complex numbers.
Could anyone list numbers not in the set of complex numbers?
No. Complex numbers is the highest set of numbers you can go, and there are no sets outside of complex numbers.
Set of real numbers and set of complex numbers are equivalent?
Real numbers are a proper subset of Complex numbers.
What year did Mr Kbh invent complex numbers?
Complex numbers were not invented by Mr KBH.
What are the kinds of complex numbers?
Complex numbers include real numbers, pure imaginary numbers, and the combination of those two.
Are complex numbers under addition and multiplication a field?
The complex numbers are a field.
Do the complex numbers for a group under binary operation ' plus '?
Yes, the complex numbers, as well as the real numbers which are a subset of the complex numbers, form groups under addition.
Which of these are complex numbers 5 3i 1 2i?
All of them. Real numbers are a subset of complex numbers.
What are set of complex number?
Complex numbers are numbers of the form (x + yi) where x and y are real numbers and i is the imaginary square root of -1. Any collection of such numbers is a set of complex numbers.
What mathematician introduced complex numbers?
Gerolamo Cardano is an Italian mathematician who introduced complex numbers. Complex numbers are those that can be expressed in the form of a+bi where a and b represent real numbers.
What is the difference between a complex number and a non real complex number?
Think of the complex numbers as points on a coordinate system. Instead of the usual x-axis you have the real numbers, instead of the y-axis, you have the imaginary numbers.The real numbers are on the horizontal axis.The imaginary numbers are on the vertical axis.The complex numbers are any number on the plane.The non-real complex are, of course, any complex numbers that are not on the real number axis - not on the horizontal axis.Think of the complex numbers as points on a coordinate system. Instead of the usual x-axis you have the real numbers, instead of the y-axis, you have the imaginary numbers.The real numbers are on the horizontal axis.The imaginary numbers are on the vertical axis.The complex numbers are any number on the plane.The non-real complex are, of course, any complex numbers that are not on the real number axis - not on the horizontal axis.Think of the complex numbers as points on a coordinate system. Instead of the usual x-axis you have the real numbers, instead of the y-axis, you have the imaginary numbers.The real numbers are on the horizontal axis.The imaginary numbers are on the vertical axis.The complex numbers are any number on the plane.The non-real complex are, of course, any complex numbers that are not on the real number axis - not on the horizontal axis.Think of the complex numbers as points on a coordinate system. Instead of the usual x-axis you have the real numbers, instead of the y-axis, you have the imaginary numbers.The real numbers are on the horizontal axis.The imaginary numbers are on the vertical axis.The complex numbers are any number on the plane.The non-real complex are, of course, any complex numbers that are not on the real number axis - not on the horizontal axis.
