Question

Вычислить: (1 - i)^42.

Answer 1

$(1-i)^2 = 1 - 2i + i^2 = -2i\\(1-i)^{42} = \underbrace{(1-i)(1-i)\cdots(1-i)}_{42} = \underbrace{(-2i)(-2i)\ldots(-2i)}_{21} = -2^{21}\cdot i^{21} =\\ -2^{21}\cdot (i^2)^{10}\cdot i = -2^{21}\cdot i$