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

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