Question

(a2+b2):(a2-b2)=(ac+bd):(ac-bd)​

Answer 1

Step-by-step explanation:

Use i2=−1 (a2+b2)(c2+d2)=[(ac+bd)+i(bc−ad)][(ac+bd)+i(bc−ad)]

⟹ (a2+b2)(c2+d2)=[(ac+bd)2−i2(bc−ad)2]

⟹ (a2+b2)(c2+d2)=(ac+bd)2+(bc−ad)2

⟹ (a2+b2)(c2+d2)=(ad−bc)2+(ac+bd)2

(a2+b2)(c2+d2)=[a2−(−b2)][c2−(−d2)]

⟹ (a2+b2)(c2+d2)=[a2−(ib)2][c2−(id)2]

⟹ (a2+b2)(c2+d2)=[(a−ib)(a+ib)][(c+id)(c−id]

⟹ (a2+b2)(c2+d2)=[(a+ib)(c−id)][(a−ib)(c+id]

⟹ (a2+b2)(c2+d2)=[ac+i(bc−ad)−i2bd)][ac−i(bc−ad)−i2bd]