-4 2. The simplest explanation is that an imaginary number is the square root of a negative number (or any even root for that matter). A complex number is generally denoted by z and the imaginary part of any complex number is represented by I[z]. The imaginary part of a complex number is, hence, a real number that is accompanied by the imaginary unit . Imaginary numbers are called imaginary because they are impossible and, therefore, exist only in the world of ideas and pure imagination. In order to find roots of complex numbers, which can be expressed as imaginary numbers, require the complex numbers to be written in exponential form. Unit Imaginary Number. Can you take the square root of −1? 13i 3. In mathematics the symbol for √(−1) is i for imaginary. (More than one of these description may apply) 1. Complex numbers are in the form a+bi, where a and b are real numbers. It takes about six paragraphs. I’m going to give the real definition and motivation for complex numbers. All imaginary numbers are complex numbers but all complex numbers don't need to be imaginary numbers. The square root of minus one √(−1) is the "unit" Imaginary Number, the equivalent of 1 for Real Numbers. In the real numbers, 1 is the real unit, and the set of all real numbers (also known as the real number line) is just the set of all multiples of this unit by a real number.In the same way, we can construct an imaginary number line consisting of all multiples of the imaginary unit by a real number. Any number of the form is called an imaginary number, and it is a complex number with an equal to zero. I sense some confusion in your question. A pure imaginary number is any complex number whose real part is equal to 0. pure imaginary number. non-real complex number. pure imaginary number an imaginary number of the form a+bi where a is 0; , A number of the form bi, where b ≠ 0. If a = 0 and b uni2260.alt1 0, the number a + bi is a pure imaginary number. A complex number a+bi in which b ≠ 0 is a non-real complex number. A pure imaginary number is any complex number whose real part is equal to 0. any number that can be written in the form of a + bi where a and b are real numbers. Imaginary numbers result from taking the square root of a negative number. 5+i Answer by richard1234(7193) (Show Source): So a complex number has a real part ("a") and an imaginary part ("bi"). If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. But in electronics they use j (because "i" already means current, and the next letter after i is j). A complex number a+bi in which a =0 and b ≠ 0 is a pure imaginary number. Question 484664: Identify each number as real, complex, pure imaginary, or nonreal complex. standard form. $\begingroup$ It should be added that in modern mathematics there is almost never any reason to talk about imaginary numbers in general -- just about everything you can say about imaginary numbers is just as valid about all the complex numbers, so it is usually said in that more general form. A complex number written in the form a+bi (or a+ib) is in standard form. For example, √-4 = 2i, which is a pure imaginary number. If you're seeing this message, it means we're having trouble loading external resources on our website. Learn about the imaginary unit i, about the imaginary numbers, and about square roots of negative numbers. Such a number, written as for some real number , is an imaginary number. Well i can! Number a + bi where a and b uni2260.alt1 0, the number +! 484664: Identify each number as real, complex, pure imaginary number to 0 ( More than one these! 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