Question

resolva as expressões 4i^23 +6i^404-100i^98

Answer 1

Conforme a regra dos números complexos:
i ² = – 1
i ³ = i2 * i = (–1) * i = –i
i 4 = i2 * i2 = (–1) * (– 1) = 1
i 5 = i4 * i = 1 * i = i
i 6 = i5 * i = i * i = i2 = –1
i 7 = i6 * i = (–1) * i = – i
i 8 = i4 * i4 = 1 * 1 = 1
i9 = i8 * i = 1 * i = i
i10 =(i2)5 = (–1)5 = –1
Diminuir numero grande: i^343 = i^3, portanto i^343 = – i
i^numero/4 = i^resto
4(i^23/4) +6(i^404/4) -100(i^98/4)
4*-i +6*1 -100*-1=
106-4i