What-are-necessary-and-sufficient-conditions-that-a-ib-n-is-cyclic-for-an-n-not-equal-to-0-

Question Number 8341 by Rasheed Soomro last updated on 09/Oct/16

What are necessary and sufficient conditions

that {(a + ib)}^{n} is cyclic for an n not equal to 0 ?

Answered by prakash jain last updated on 09/Oct/16

∣ a + i b ∣= 1 \Rightarrow \sqrt{a^{2} + b^{2}} = 1

The above is necessary and ? sufficient

condition .

then if

a r c t a n (b, a) = \frac{2 π}{k} then

{(a + b i)}^{j + m k} = (a + b i), j, m, k \in Z, j \in [0, k - 1]