i⁻³ = i¹ = i⁵ = i⁹ = +i i⁻² = i² = i⁶ = i¹⁰ = –1 i⁻¹ = i³ = i⁷ = i¹¹ = –i i⁰ = i⁴ = i⁸ = i¹² = +1 i^(4n) = 1 (n is integer) i^(4n + 1) = i i^(4n + 2) = -1 i^(4n + 3) = -i √i = ±(√2/2)(1+i) √(x+iy) = √[ (r+x)/2 ] ± i √[ (r–x)/2 ] with r = √(x² + y²) ∛i = –i, ½+√3/2, –½+√3/2 ∛(–1) = –1, ½–i√3/2, and ½–i√3/2 ∛(–N) = ∛N[ –1, ½–i√3/2, and ½–i√3/2 ] de Moivre's formula, states that for any complex number (and, in particular, for any real number) x and integer n it holds that" (cos x + i sin x)ⁿ = cos (nx) + i sin (nx) i = √(–1) The property √(ab) = √a √b is valid when a and b are both non-negative real numbers. |
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