1.

If a+ib/c+id=x+iy prove that X²+y²=a²+b²/c²+d²​

Answer»

Answer:

LHS = RHS

Step-by-step EXPLANATION:

 Here,

⇒ ( a + bi ) / ( c + ID ) = x + iy

 Using the properties of complex NUMBERS, we know :  

  if z = a / d  then  | z | = | a | / | d |    where z, a , d are  complex numbers.

Using the same property;

 Modulus of LHS = Modulus of RHS

\implies \mathrm{\bigg| \dfrac{a+bi}{c+di} \bigg| =|x+iy|}

\implies \mathrm{\dfrac{\sqrt{a^2+b^2}}{\sqrt{c^2+d^2 } }=\sqrt{x^2 +y^2}}\\\\\\\implies \mathrm{\dfrac{a^2 +b^2}{c^2+d^2}=x^2+y^2 }

LHS = RHS


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