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$