3 If k+k+z2=z2∀ k∈R-1, then argz isA5π4 - Maths - Complex Numbers and Quadratic Equations

Question

3   I f   k + k + z 2 = z 2 ∀   k ∈ R -
1 ,   t h e n   a r g z   i s A 5 π 4  
                 
                 
                 
          B π 3 C π 2  
                 
                 
                 
              D - π 2

Shivam Mishra · Accepted Answer

Dear Student,
Please find below the solution to the asked query:

We havek+k+z2=z2
 k∈R+⇒k+k+z2=z2⇒z2-z2+k=k⇒z2-0-z2--k=kLet z2=w⇒w-0-w--k=kwhich will be true when w=-kz2=-k⇒z=±ik which is purely imaginary, hence argz can be π2or -π2

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3 . I f k + k + z 2 = z 2 ∀ k ∈ R - 1 , t h e n a r g z i s A 5 π 4 B π 3 C π 2 D - π 2

$3 . I f k + |k + z^{2}| = {|z|}^{2} \forall k \in R^{- 1}, t h e n a r g (z) i s (A) \frac{5 π}{4} (B) \frac{π}{3} (C) \frac{π}{2} (D) - \frac{π}{2}$