Question

that
if
show
x +iy =(a +ib)²,
x² + y² = (a² + b²)²​

Answer 1

ok

Step-by-step explanation:

first way

if (a+ib)²=x+iy then a²+2abi+(ib)²=a²-b²+i2ab=x+iy so

a²-b²=x and 2ab=y

x²+y²=(a²-b²)²+(2ab)²=a^4 -2a²b²+b^4+4a²b²=a^4+2a²b²+b^4=(a²+b²)²

second way

if (a+ib)²=x+iy then |(a+ib)²|=|x+iy| so |(a+ib)|²=|x+iy|

so (|(a+ib)|²)²=|x+iy|² therefore (a²+b²)²=x²+y²