This all looks like it is working well, but some things break down for square roots of negative numbers. Discover the magic of the imaginary unit i This lesson dives into simplifying the square root of negative numbers using i, the principal square root of -1. If #a < 0# then we define #sqrt(a)# to be the principal square root of #a#, lying on the positive part of the imaginary ( #y#) axis. Step 2: SeparateSeparate the perfect square, 64, from the other factor, -1. Sal explains 'as I said in the last video, the principal root of X squared is going to be the absolute value of X, just in case X is a negative number'. In mathematics, simplifying the square root of negative numbers involves the use of the imaginary unit i, which is the square root of -1. Step 1: FactorFirst, factor 64, looking for perfect squares. Since 64 is the square root of a negative number, it is an imaginary number. Algebra II Practice N.CN.A.2: Square Roots of Negative Numbers NAME: 1.Simplify. In mathematics the symbol for (1) is i for. If #a >= 0# then #sqrt(a)# means the non-negative square root of #a#, which lies on the part of the Real line at and to the right of the origin #0#. Study with Quizlet and memorize flashcards containing terms like i, Now lets use the same rules to simplify 64. The square root of minus one (1) is the unit Imaginary Number, the equivalent of 1 for Real Numbers. The unit in the #y# (imaginary) direction is the number #i#. The unit in the #x# direction is the number #1#. If #x# is a Real number then #x^2 >= 0#, so we need to look beyond the Real numbers to find a square root of #-1#.Ĭomplex numbers can be thought of as an extension of Real numbers from a line to a plane. Like all non-zero numbers, #-1# has two square roots, which we call #i# and #-i#. To reduce a radical expression to simplified form, factor out as many perfect squares as possible from within the radical, and multiply by a form of 1 to remove. I really dislike the expression " the square root of minus one".
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