Grade 11Algebra
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?
4 Answers
Naga 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
Other Related Questions on algebra
How do you write “the product of 18 and q” as an algebraic expression?
How do you write “the product of 18 and q” as an algebraic expression?
algebra
Last Activity: 2 Years ago