Resolvendo livro de matemática - Parte 245 скачать в хорошем качестве

Resolvendo livro de matemática - Parte 245

2 (2x - 3y) + 5i = -4 + (x + 2y)i 2x - 3y = -4 x + 2y = 5 2x - 3y = -4 -2x - 4y = -10 -7y = -14 y = 2 x = 1 3 z = a + bi zi + 2z' + 1 - i = 0 zi + 2z' = -1 + i (a + bi)i + 2(a - bi) = -1 + i ai - b + 2a - 2bi = -1 + i 2a - b + (a - 2b)i = -1 + i 2a - b = -1 a - 2b = 1 2a - b = -1 -2a + 4b = -2 3b = -3 b = -1 a = -1 z = -1 - i 4 (5 + 5i)/(3 - 4i)+20/(4 + 3i) (5 + 5i)/(3 - 4i)*(3+4i)/(3+4i) (5 + 5i)(3 + 4i) 15 + 20i + 15i - 20 -1 + 7i/5 20/(4 + 3i)*(4-3i)/(4-3i) 16 - 12i/5 z = (-1 + 7i)/5+(16 - 12i)/5 z = (15- 5i)/5 z = 3 - i 5 (2 + z)(1 - i) - (zi - 1)(1 + i) = 4 - i (2 + z)(1 - i) 2 - 2i + z - zi (zi - 1)(1 + i) zi - z - 1 - i 2 - 2i + z - zi - zi + z + 1 + i = 4 - i 2z - 2zi = 1 z(2 - 2i) = 1 z = 1/(2 - 2i) 1/(2 - 2i)*(2+2i)/(2+2i) 2 + 2i/8 z = 1/4+1/4i 6 (1 - i)/(1 + i)+(1 + i)/(1 - i) (1 - i)/(1 + i)*(1-i)/(1-i) 1 - 2i - 1/2 = -i (1 + i)/(1 - i)*(1+i)/(1+i) 1 + 2i - 1/2 = i z = 0 7 z = (2x + 4) - (y - 3)i 2x + 4 = 0 x = -2 -y + 3 = 0 y = 3 8 (1 + i)²(1 - i)² ((1 + i)(1 - i))² (1 + 1)² = 4 9 (a + 2i)i³ - (-3 + 3i) = b + 2i -b - ai = -5 + 5i b = 5 a = -5 10 z = (-1 + 3i)/(4 + ki) (-1 + 3i)/(4 + ki)*(4-ki)/(4-ki) (-1 + 3i)(4 - ki) -4 + ki + 12i + 3k z = (3k - 4 + (k+12)i)/(k^2+ 16) k = -12 11 (x+ i)/(1- i)=(1- i)/(1+ i) (x+ i)/(1- i)*(1+i)/(1+i) (x + i)(1 + i) x + xi + i - 1/2 (1- i)/(1+ i)*(1-i)/(1-i) -2i/2 = -i (x + xi + i - 1)/2 = -i x + xi = 1 - 3i x(1 + i) = 1 - 3i x = (1 - 3i)/(1 + i) (1 - 3i)/(1 + i)*(1-i)/(1-i) (1 - 3i)(1 - i) 1 - i - 3i - 3/2 z = -1 - 2i 12 z = (3 - i)/2i 2z' - 1/z (3 - i)/2i*(-2i)/(-2i) -6i - 2/4 z = -1/2-3/2i 2z' = -1 + 3i 1/z=(1/1)/((-1 - 3i)/2) 1/z = 2/(-1 - 3i) 2/(-1 - 3i)*(-1+3i)/(-1+3i) -1 + 3i/5 -1 + 3i + (1 - 3i)/5 z = (-4 + 12i)/5 13 z = (4 - mi)/(2 + 3i) (4 - mi)/(2 + 3i)*(2-3i)/(2-3i) (4 - mi)(2 - 3i) 8 - 12i - 2mi - 3m (8 - 3m + (-12 - 2m)i)/13 m = -6 14 z = (1 - i)/i (1 - i)/i*(-i)/(-i) z = -1 - i z' = -1 + i p = √2 cos(x) = -√2/2 180x = 135𝝿 x = 3𝝿/4 z' = √2(cos(3𝝿/4) + isen(3𝝿/4)) 15 z1 = -1 + i z2 = 1 + i w = z2 - z1' w = 1 + i - (-1 - i) w = 2 + 2i p = 2√2 cos(x) = √2/2 x = 45° 45 = 𝝿/4 x = 𝝿/4 w = 2√2(cos(𝝿/4) + isen(𝝿/4)) 16 z²' = ? z = a(cos(x) + isen(x)) a = 2 x = 𝝿/8 z² = 4(cos(𝝿/4) + isen(𝝿/4)) p = 4 a = 4cos(𝝿/4) a = 2√2 z² = 2√2 + 2√2i z²' = 2√2 - 2√2i