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# Complex or imaginary numbers - A complete course in algebra

No, I'm not making this up. Here it is: That's an " i " for imaginary number. So, what's the i? For the imaginary number system, we just define it this way. So far, in your math career, you've been working with real numbers.  (Even though some of your answers on math tests have been unreal.  haha!) All the guys that appear on the number line are real numbers (in the real number system You've probably been told (even by me) that you couldn't do yet because of that negative sign.  The reason is that the answer isn't a real number.  Yes, there IS an answer!  (Try to calm down - I know this is terribly exciting.)  There is an answer.  and it's imaginary.  30, the defining property of i, the square root of a negative number, powers of i, algebra with complex numbers. The real and imaginary components, complex conjugates, i N algebra, we want to be able to say that every polynomial equation has a solution; specifically, this one: x 2 1 0.

To cover the answer again, click "Refresh" Reload. Do the problem yourself first! A) i 2  1 b) i 2 i 2 i 2 2(1) 2 c) (3 i )2  32 i 2 9 d) 5 i 4 i 20 i 2 20 The square root of a negative number If a radicand is negative -,  where a 0, - then. We may add it, subtract it, multiply it, and so on. The complex number i turns out to be extremely useful in mathematics and physics. Example 1. 3 i 4 i 12 i 2 12(1) 12.  (Any number with exponent