**Cyclic Nature of the powers of "**yellowcomic.com Topical synopsis | Algebra 2 overview | MathBits" Teacher resources

*i "***Terms of Use call Person:**Donna Roberts

When the imagine unit,

*i*, is elevated to increasingly higher powers, a cyclic (repetitive) pattern emerges. Remember the

*i*2 = -1.

You are watching: I to the power of 6

*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).See more: Percentage Calculator: What Is 10 Percent Of 60 = 6, Solved: What Is 10 Percent Of 60 = 6 |

simplify

*i*87

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. |

**contact Person:**Donna Roberts