Question

If x+iy=(a+ib) ^2, prove that x^2 +y^2 =(a^2+b^2)^2​

Answer 1

Step-by-step explanation:

X+iy=(a+ib)^2

x+iy=a^2-b^2+2iab. {i^2=-1}

compare real part and imaginary part

x=a^2-b^2 , y=2ab

squaring on both side (xy terms)

x^2=(a^2-b^2)^2

y^2=4a^2b^2

x^2+y^2=(a^2-b^2)^2+4a^2b^2

x^2+y^2=(a^2+b^2)^2

Hence proved