The real and imaginary components. The number is defined as the solution to the equation = − 1 . Let's explore more about imaginary numbers. Imaginary numbers, as the name says, are numbers not real. Imaginary numbers result from taking the square root of a negative number. (More than one of these description may apply) 1. Question 484664: Identify each number as real, complex, pure imaginary, or nonreal complex. Here is what is now called the standard form of a complex number: a + bi. (iii) Find the square roots of 4 4+i (iv) Find the complex number … Example 2. Examples for Complex numbers Question (01) (i) Find the real values of x and y such that (1 ) 2 (2 3 ) 3 3 i x i i y i i i i − + + + + =− − + (ii) Find the real values of x and y are the complex numbers 3−ix y2 and − − −x y i2 4 conjugate of each other. Example - 2−3 − … 5+i Answer by richard1234(7193) (Show Source): Definition: Imaginary Numbers. and are real numbers. b (2 in the example) is called the imaginary component (or the imaginary part). The union of the set of all imaginary numbers and the set of all real numbers is the set of complex numbers. It is the real number a plus the complex number . In these cases, we call the complex number a number. Often is … As a brief aside, let's define the imaginary number (so called because there is no equivalent "real number") using the letter i; we can then create a new set of numbers called the complex numbers.A complex number is any number that includes i.Thus, 3i, 2 + 5.4i, and –πi are all complex numbers. Imaginary numbers are called imaginary because they are impossible and, therefore, exist only in the world of ideas and pure imagination. For example, 3 + 2i. Since is not a real number, it is referred to as an imaginary number and all real multiples of (numbers of the form , where is real) are called (purely) imaginary numbers. For example, 17 is a complex number with a real part equal to 17 and an imaginary part equalling zero, and iis a complex number with a real part of zero. Another Frenchman, Abraham de Moivre, was amongst the first to relate complex numbers to geometry with his theorem of 1707 which related complex numbers and trigonometry together. For example, it is not possible to find a real solution of x 2 + 1 = 0 x^{2}+1=0 x 2 + 1 = 0. a—that is, 3 in the example—is called the real component (or the real part). (Note: and both can be 0.) This is also observed in some quadratic equations which do not yield any real number solutions. A pure imaginary number is any complex number whose real part is equal to 0. ... we show more examples of how to use imaginary numbers to simplify a square root with a negative radicand. 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