Question

Sa se rezolve :
$(1 + i) {}^{10} + (1 - i) {}^{10}$
​

Answer 1

Se stie ca i = √-1 si ca (a + b)^2 = a^2 +2ab + b^2.

(1 + i)^10 + (1 - i)^10 = ((1 + √-1)^2)^5 + ((1 - √-1)^2)^5 = (1^2 + 2√-1 + (√-1)^2)^5 +  (1^2 - 2√-1 + (√-1)^2)^5 = (1 - 1 + 2√-1)^5 + (1 - 1 - 2√-1)^5 = (2√-1)^5 + (- 2√-1)^5 = 32*(-1)*√-1 - 32*(-1)*√-1 = 0.

Raspuns: (1 + i)^10 + (1 - i)^10 = 0.

Sper ca te-am ajutat!