Question

if x+iy = (3-4i)(7+24i)/4-3i,then x²+y²= ?​

Answer 1

Step-by-step explanation:

If (x+iy)2=7+24i , then what would be the value of (7+−576−−−−√)12−(7−−576−−−−√)12 ?

(x+iy)^2 = 7+24i

x^2+(iy)^2+(2*x*iy) = 7 +24i

x^2 - y^2 + 2xyi = 7 +24i

On comparing LHS and RHS

x^2 - y^2 = 7 (eq 1)

2xy = 24 ; xy =12 ; y = 12 /x (eq 2)

2 unknowns 2 equations, on solving them you get:

Solution 1: x = 4 (plus or minus) and y = 3 (plus or minus)

Solution 2: x = 3i and y = 4i

(7 + √-576) ^1/2 = (7 + 24i)^1/2 = ((x+iy)^2)^1/2 = x+iy

(7 - √-576) ^1/2 = (7 -24i)^1/2 = (x^2 - y^2 - 2xyi)^1/2 = ((x -iy)^2)^1/2 = x - iy

So, (7 + √-576) ^1/2 - (7 - √-576) ^1/2 = x +iy - (x -iy) = 2iy

Solution 1: 2*i*3(plus or minus) = 6i (plus or minus)

Solution 1: 2*i*(4i) = -8