Imaginary Numbers Raised To A Power. One can also show that the definition of e x for complex numbers x still satisfies the usual properties of exponents so we can find e to the power of any complex number b ic as follows. It is imaginary because you can t have the square root of 1.
Let s plot some more. The answer is a combination of a real and an imaginary number which together is called a complex number. Here we show the number 0 45 0 89 i which is the same as e 1 1i.
There is nothing you multiply by itself to get a negative number because a negative times a negative is a positive.
E pi i 1 is a definition due to a property that i gives. You can raise i to any positive integer value using a ti 84 calculator unfortunately the older model calculators will only give an exact answer i 1 i 1 up to a power of 6. The newer ti 84 ce will give an exact answer i 1 i 1 up to a power of 100. When a number is raised to the power of i the number itself becomes imaginary.