When the imagine unit, i, is elevated to increasingly higher powers, a cyclic (repetitive) pattern emerges. Remember the i 2 = -1.
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Simplifying powers of i: friend will must remember (or establish) the strength of 1 through 4 of i to acquire one bike of the pattern. From the list that values, friend can easily determine any kind of other positive integer powers of i.
Method 1: once the exponent is higher than or same to 5, usage the reality that i 4 = 1 and the rules because that working through exponents to simplify higher powers of i. Break the power under to display the determinants of four.
when raising i to any positive essence power, the answer is constantly i, -1, -i or 1.
Another way to look in ~ the simplification: Method 2: divide the exponent by 4: • if the remainder is 0, the answer is 1 (i0). • if the remainder is 1, the prize is i (i1). • if the remainder is 2, the prize is -1 (i2). • if the remainder is 3, the price is -i (i3).
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|By Method 1: breakdown the strength to show components of 4. (84 is the largest multiple of 4) |
|By Method 2: divide the strength by 4 to find the remainder. 87 ÷ 4 = 21 through remainder 3 The price is i3 i beg your pardon is -i.|
You can raise i to any kind of positive integer value making use of a TI-84+ calculator. Unfortunately, the older model calculators will only give an exact answer ( i, 1, -i, -1) as much as a power of 6. The more recent TI-84+CE will certainly give specific answer ( i, 1, -i -1) approximately a strength of 100. Beyond these powers, the calculators will provide an calculation (in scientific notation) that will must be interpreted as to whether the price is i, 1, -i , or -1. review more.