Try. Always positive, or zero. For example, simplify i²⁷ as -i. Four numbers on the real line are multiplied by integer powers of the imaginary unit, which corresponds to rotations by multiples of the right angle. You can add, subtract, multiply and divide them in any combination.

Rules for Imaginary Numbers Imaginary and complex numbers work much like real ones. It seems like we cannot multiply a number by itself to get a negative … Although Greek mathematician and engineer Hero of Alexandria is noted as the first to have conceived these numbers, Rafael Bombelli first set down the rules for multiplication of complex numbers in 1572. Therefore, the rules for some imaginary numbers are: i = √-1 i 2 = -1 i 3 = -i i 4 = +1 i 4n = 1 i 4n-1 = -i

Powers of the imaginary unit CCSS Math: HSN.CN.A.1, HSN.CN.A.2, HSN.CN.A Learn how to simplify any power of the imaginary unit i. They follow the normal rules of math, with the wrinkle that imaginary numbers, when squared, give a negative answer. At the time imaginary numbers, as well as negative numbers, were poorly understood and regarded by some as fictitious or useless, much as zero once was. Many other mathematicians were slow to adopt the use o… The concept had appeared in print earlier, for instance in work by Gerolamo Cardano.