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?
Chirag Arora , 8 Years ago
Grade 11
Algebra> Let the complex number Z satisfy the equa...
4 AnswersNaga sree harsha reddy
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
real partpart of is 24..we will get by solving =625....|z|^2 √a^2+7^2 +a=1;hence
aravind m t
real partpart of is 24..we will get by solving |z|^2 √a^2+7^2 +a=1....;hence|z|^2 =625
Samyak Jain
z + |z| = 1 +7i ….......... (1)
Let z = x + iy 
|z| = 
(x2 + y2)
(1) can be rewritten as x + iy + x2 + y2 = 1 + 7i
Equate real and imaginary parts of LHS & RHS.
x2 + 49 = (1 – x)2 i.e. x2 + 49 = 1 – 2x + x2
49 = 1 – 2x
2x = – 48 or x = – 24
= 576 + 49 = 625
|z| = 25
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