Question

Determine o número z, tal que zi + 2z = 4-i​

Answer 1

Resposta:

·⠀⠀⠀⠀z = 7/5 – 6i/5⠀⠀⠀⠀

Explicação passo-a-passo:

·⠀⠀⠀⠀

·⠀⠀⠀⠀zi + 2z = 4 – 1 , z = ? = a + bi

·⠀⠀⠀⠀(a + bi)i + 2(a + bi) = 4 – 1

·⠀⠀⠀⠀ai – b + 2a + 2bi = 4 – 1

·⠀⠀⠀⠀(2a – b) + (2b + a)i = 4 – 1

·⠀⠀⠀⠀

·⠀⠀⠀⠀{2a - b = 4

·⠀⠀⠀⠀{2b + a = – 1 => a = – 1 – 2b

·⠀⠀⠀⠀

·⠀⠀⠀⠀2(– 1 – 2b) – b = 4

·⠀⠀⠀⠀– 2 – 4b - b = 4

·⠀⠀⠀⠀– 5b = 6

·⠀⠀⠀⠀b = – 6/5

·⠀⠀⠀⠀

·⠀⠀⠀⠀a = – 1 – 2(– 6/5)

·⠀⠀⠀⠀a = – 1 + 12/5

·⠀⠀⠀⠀a = 7/5

·⠀⠀⠀⠀

·⠀⠀⠀⠀z = 7/5 – 6i/5