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Let the complex number Z satisfy the equation z + |z| = 1 +7i then the value of |z|^2 is?

Let the complex number Z satisfy the equation 
z + |z| = 1 +7i then the value of |z|^2 is?

Grade:11

4 Answers

Naga sree harsha reddy
21 Points
6 years ago
Let z=x+it,then |z|=√x^2+y^2=1; compare real terms i.e;x+√x^2+y^2=1; and compare imaginary part with imaginary part i.e;y=7 put in 1 and get value of x as |z| is required;find √x^2+y^2
aravind m t
14 Points
6 years ago
real partpart of is 24..we will get by solving =625....|z|^2 √a^2+7^2 +a=1;hence 
aravind m t
14 Points
6 years ago
real partpart of is 24..we will get by solving |z|^2 √a^2+7^2 +a=1....;hence|z|^2 =625
Samyak Jain
333 Points
5 years ago
z + |z| = 1 +7i                   ….......... (1)
Let z = x + iy  \therefore  |z| = \sqrt{}(x+ y2) 
(1) can be rewritten as x + iy + \sqrt{}x+ y = 1 + 7i
Equate real and imaginary parts of LHS & RHS.
\therefore y = 7 ;  x + \sqrt{}(x+ y2) = 1  or  x + \sqrt{}(x+ 49) = 1
x+ 49 = (1 – x)2  i.e.  x+ 49 = 1 – 2x + x2
49 = 1 – 2x  
2x = – 48   or    x = – 24
\therefore |z| = \sqrt{}(x+ y2)    =  \sqrt{}(– 24)+ 72  
        = \sqrt{}576 + 49   =  \sqrt{}625
   |z|  =  25

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