1) (-1+i)^5
2) 2x + (1+i) (x+y) = 7+i
3) 5 / 1+2i

Предыдущий
вопрос Следующий
вопрос

1) (-1+i)^5
= (-1+i)(-1+i)(-1+i)(-1+i)(-1+i)
= (1 - 2i + i^2)(-1+i)(-1+i)
= (-1 - 2i)(-1+i)
= 1 + i + 2i - 2i^2
= 1 + 3i + 2
= 3 + 3i

2) 2x + (1+i) (x+y) = 7+i
Expanding the equation:
2x + x + y + ix + iy = 7 + i
Combining like terms:
3x + y + (i)(x + y) = 7 + i
3x + y + i(x + y) = 7 + i

3) 5 / (1+2i)
To simplify the expression, multiply the numerator and denominator by the conjugate of the denominator:
(5 / (1+2i)) * ((1-2i) / (1-2i))
= 5(1-2i) / (1^2 - (2i)^2)
= 5 - 10i / (1 - 4i^2)
= 5 - 10i / (1 + 4)
= 5 - 10i / 5
= 1 - 2i