Subject: my name is gary i have a math?

i am not a student i am just some one that heard something and i can't be sure on the ? is what is the square root of -1? i think it is -1 but not sure can you let me know please thank you

Hi Gary,

There are different types of numbers that we use. For example

  • Whole numbers: 1, 2, 3,...
  • Integers: ...-3, -2, -1, 0, 1, 2,...
  • Fractions, sometimes called rational numbers: 2/3, -3/5,... Rational numbers are numbers that can be written as an integer divided by a non-zero integer. Rational numbers include the integers since, for example, 5 = 5/1.
  • Irrational numbers: numbers that cannot be written as an integer divided by an integer. Examples are the square root of 2, the square root of 7 and pi.
  • Real numbers: the rational and irrational numbers

None of the numbers mentioned above has the property that its square is -1. In other words the square root of -1 is not a real number. It is however useful to have a "number" which is the square root of -1 so mathematicians have defined a "number" usually designated i, or sometimes j, that has the property that i*i = -1 (* is multiplication). This then generates a new type of numbers called the complex numbers. Complex numbers are numbers that can be written a + b*i where a and b are real numbers. For example 5 + 3*i or 3/5 -(2/3)*i.

Complex numbers are useful in many areas of mathematics, Science and Engineering. Some aspects of electricity and magnetism are best understood using complex numbers. The place where students in high school see complex numbers is in the study of quadratic equations. If you consider real numbers only, then some quadratic equations have solutions and some do not. If you include complex numbers then every quadratic equation has a solution, and this fact helps unify the study of such equations.

I hope this helps,
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