Question

Calcule os valores de a e b na equação :. ( 1 + i )^9 x ( 2 - i )^3/(-1-i) ^10= a + bi

Answer 1

Resposta:

(1 + i )^9 x ( 2 - i )^3/(-1-i)^10 = a + bi  

(1 + i )^9 * (2-i)³/(1+i)¹º

(2-i)³/(1+i) = a + bi  

(2-i)³ = (a + bi)*(1+i)

(2-i)³ =a+ai+bi-b

8-3*2²*i+3*2*i²-i³ = a-b +i(a+b)

8 -12i - 6+i =a-b+i(a+b)

2 -11i =a-b +i(a+b)

a-b=2   (i)

a+b=-11   (ii)

(i) +(ii)

2a =-9 ==>a=-9/2

Usando (i) ==> -9/2-b=2 ==>b=-9/2-2 =b

b=-13/2

a+bi =-9/2 -13i/2  é a resposta