Imaginary numbers result from taking the square root of a negative number. Imaginary numbers are called imaginary because they are impossible and, therefore, exist only in the world of ideas and pure imagination. I sense some confusion in your question. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. Learn about the imaginary unit i, about the imaginary numbers, and about square roots of negative numbers. $\begingroup$ 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. So a complex number has a real part ("a") and an imaginary part ("bi"). pure imaginary 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. 13i 3. A pure imaginary number is any complex number whose real part is equal to 0. Any number of the form is called an imaginary number, and it is a complex number with an equal to zero. The square root of minus one √(−1) is the "unit" Imaginary Number, the equivalent of 1 for Real Numbers. A complex number a+bi in which a =0 and b ≠ 0 is a pure imaginary number. Complex numbers are in the form a+bi, where a and b are real numbers. It takes about six paragraphs. A pure imaginary number is any complex number whose real part is equal to 0. A complex number written in the form a+bi (or a+ib) is in standard form. standard form. -4 2. I’m going to give the real definition and motivation for complex numbers. A complex number a+bi in which b ≠ 0 is a non-real complex number. 5+i Answer by richard1234(7193) (Show Source): non-real complex number. any number that can be written in the form of a + bi where a and b are real numbers. The imaginary part of a complex number is, hence, a real number that is accompanied by the imaginary unit . All imaginary numbers are complex numbers but all complex numbers don't need to be imaginary numbers. Well i can! If you're seeing this message, it means we're having trouble loading external resources on our website. Such a number, written as for some real number , is an imaginary number. Can you take the square root of −1? But in electronics they use j (because "i" already means current, and the next letter after i is j). A complex number is generally denoted by z and the imaginary part of any complex number is represented by I[z]. Question 484664: Identify each number as real, complex, pure imaginary, or nonreal complex. Unit Imaginary Number. If a = 0 and b uni2260.alt1 0, the number a + bi is a pure imaginary number. (More than one of these description may apply) 1. For example, √-4 = 2i, which is a pure imaginary number. 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. 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. In mathematics the symbol for √(−1) is i for imaginary. The simplest explanation is that an imaginary number is the square root of a negative number (or any even root for that matter). Exist only in the form a+bi ( or a+ib ) is in standard form and the imaginary unit pure.. This message, it means we 're having trouble loading external resources on our.! Such a number, is an imaginary number, written as for some real number, is an number. J ( because `` i '' already means current, and it is a pure imaginary number real.! 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