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Solve the system of equations Re(z2)=0,z=2 .

0 2 Views | Posted 3 months ago
Asked by Shiksha User

  • 1 Answer

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    Answered by

    Payal Gupta | Contributor-Level 10

    3 months ago

    This is a long answer type question as classified in NCERT Exemplar

    G i v e n     t h a t : R e ( z 2 ) = 0     a n d     | z | = 2 L e t     z = x + y i ∴                                               | z | = x 2 + y 2 ⇒             x 2 + y 2 = 2         ⇒ x 2 + y 2 = 4                                                                                   … ( i ) Since  z=x+yi                       z 2 = x 2 + y 2 i 2 + 2 x y i               ⇒ z 2 = x 2 − y 2 + 2 x y i ∴       R e ( z 2 ) = x 2 − y 2 ⇒ x 2 − y 2 = 0                                                                                                                                                                         … ( i i ) F r o m     e q n . ( i )     a n d     ( i i ) ,     w e     g e t x 2 + y 2 = 4                   ⇒ 2 x 2 = 4             ⇒ x 2 = 2           ⇒ x = ± 2     a n d     y = ± 2 H e n c e ,     z = ± 2 ± i 2 ,     − 2 ± i 2 .

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