Question

If (a+ib) (c+id)(e+if)(g+ih)= A+in ,then show that

(a^2+b^2)(c^2+d^2)(e^2+f^2)(g^2+h^2)= A^2+ B^2

Answer 1

(a + ib)(c + id)(e + if)(g + ih) = A + iB

take modulus both sides,

|(a + ib)(c + id)(e + if)(g + ih)| = |A+iB|

we know,
|z1.z2.z3.......zn| = |z1|.|z2|........|zn| use this here,


|a+ib|.|c+id|.|e+if|.|g+ih| = |A+iB|

we also know,
|x + iy| = √(x²+y²) use it here,

√(a²+b²).√(c²+d²).√(e²+f²).√(g²+h²) = √(A²+B²)

squaring both sides,

(a²+b²).(c²+d²).(e²+f²).(g²+h²) = A²+B²
hence, proved//

Answer 2

See the attachment I hope it will help you^_^


Step1: Take conjugate Both sides.

step 2: Multiply both 1and 2


THANKS ❤:)


#Nishu HarYanvi ♥