complex numbers??what are they?

Answer 1

Complex numbers are hybrids which are combinations of real and imaginary numbers. They are in the form a + bi, where "a" and "b" are real numbers, and "i" is the imaginary number, √-1.

Complex numbers can be used to find roots (numbers which when substituted into an equation yield 0) of equations which have no pure real numbers for roots. For example, the equation x² + 5x + 7 = 0 has no pure real roots. When we substitute the values from this equation, where a = 1, b = 5, and c = 7 into the quadratic formula, x = {- b ± √[(b)² - (4)(a)(c)]}/ 2a, we get this:

x = {-5 ± √[(5)² - (4)(1)((7)]} / [ 2(1)]
x = (-5 ± √-3) / 2
x = [-5 ± (√3*√-1)] / 2
x = [-5 ± (√3) i] / 2
x = (-5/2) ± (√3)/2 i
x = (-5/2) + (√3)/2 i or x = (5/2) - (√3)/2 i.

Notice that -5/2 and ±√3/2 are real numbers, although the last number is irrational. The solution is in the form a + bi, a - bi, where a = -5/2 and b = √3/2 or b = -√3/2. If you were to substitute these values into the original equation, a true statement would result.

Answer 2

complex numbers are a mathematical construct used to represent "imaginary space". Since by definition the square of a number is always positive, you can't take the square root of a negative number and get a "real" value.

So a complex number (also called imaginary number) is any result of solving an equation that involves taking the square root of a negative number. This is usually denoted as lower case i. where i = SQRT(-1).

It seems totally useless to know about complex numbers, but they are necessary to solve many engineering problems, particularly those related to vibratory responses, and signal analysis amongst other things.

Answer 3

Complex numbers are numbers that have the form of:

a+bi

Where i=√(-1)

Answer 4

it's like a+bi
a & b are the real #'s & i is the imaginary unit.