# pure imaginary number examples

-4 2. Imaginary numbers are called imaginary because they are impossible and, therefore, exist only in the world of ideas and pure imagination. b (2 in the example) is called the imaginary component (or the imaginary part). and are real numbers. This is unlike real numbers, which give positive results when squared. It is the real number a plus the complex number . For example, 3 + 2i. The number is defined as the solution to the equation = − 1 . 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. 13i 3. 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. a—that is, 3 in the example—is called the real component (or the real part). Here is what is now called the standard form of a complex number: a + bi. A pure imaginary number is any number which gives a negative result when it is squared. 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. (More than one of these description may apply) 1. (Note: and both can be 0.) Because of this we can think of the real numbers as being a subset of the complex numbers. Example 2. the real parts with real parts and the imaginary parts with imaginary parts). Often is … pure imaginary Next, let’s take a look at a complex number that has a zero imaginary part, z a ia=+=0 In this case we can see that the complex number is in fact a real number. The real and imaginary components. 5+i Answer by richard1234(7193) (Show Source): The union of the set of all imaginary numbers and the set of all real numbers is the set of complex numbers. Let's explore more about imaginary numbers. Simplify the following product: $$3i^5 \cdot 2i^6$$ Step 1. Group the real coefficients and the imaginary terms  \blue3 \red i^5 \cdot \blue2 \red i^6 \\ ( … Example - 2−3 − … In these cases, we call the complex number a number. Definition: Imaginary Numbers. Imaginary numbers, as the name says, are numbers not real. This is also observed in some quadratic equations which do not yield any real number solutions. Imaginary numbers result from taking the square root of a negative number. ... we show more examples of how to use imaginary numbers to simplify a square root with a negative radicand. (iii) Find the square roots of 4 4+i (iv) Find the complex number … Addition / Subtraction - Combine like terms (i.e. 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. 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