Question

Efetue(números complexos)
a) i^-98/i^-34
b) i^132 + i^61/i^42

Answer 1

a) $\frac{i^{-98}}{i^{-34}} =i^{-98}i^{34} =i^{-98+34}=i^{-64}= \\ \\ = i^{-(4.16)}=(i^4)^{-16}$

$Como \ i^4 = 1,$

$\frac{i^{-98}}{i^{-34}} = 1^{-16} = 1$

b) $i^{132} + \frac{i^{61}}{i^{42}} = (i^4)^{33} + i^{61-42} = 1^{33} + i^{19} = \\ \\ = 1 + i^{16+2+1} = 1 + i^{16}i^{2}i^1 = 1 + (i^4)^{4}i^{2}i^1$

$Como \ i^2 = - 1,$

$i^{132} + \frac{i^{61}}{i^{42}} = 1+1^{4}(-1)i = 1-i$