Grade 12th passAlgebra
If k +|k+z^2|=|z|^2 for all k belongs to negative real number then arg(z) isA)5π/4B)π/3C)π/2D)-π/2
If k +|k+z^2|=|z|^2 for all k belongs to negative real number then arg(z) is
A)5π/4
B)π/3
C)π/2
D)-π/2
1 Answer
Aditya Gupta
write |k+z^2|=|z|^2 – k
let z= re^ix
now square both sides and using euler identity e^iy= cisy,
k^2+r^4+kr^2(2cos2x)= k^2+r^4 – 2kr^2
cos2x= – 1
2x= pi
or x= pi/2
also, – pi/2 is also possible because cos2x= – 1 also implies that 2x= – pi
or x= – pi/2 will also be a solution
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