4-1.Complex numbers
medium

यदि ${z_1},{z_2}$ दो सम्मिश्र संख्याएँ इस प्रकार हैं कि ${z_1} + {z_2}$ तथा ${z_1}{z_2}$ दोनों वास्तविक हैं, तब

A

${z_1} = - {z_2}$

B

${z_1} = {\bar z_2}$

C

${z_1} = - {\bar z_2}$

D

${z_1} = {z_2}$

Solution

(b) माना ${z_1} = a + ib,{z_2} = c + id$, तब  ${z_1} + {z_2}$ वास्तविक है   

 $⇒(a + c) + i(b + d)$ वास्तविक है

$⇒ b + d = 0$   $⇒ d =  – b$                …..(i)

${z_1}{z_2}$ वास्तविक है  $⇒ (ad – bd) + i(ac + bc)$ वास्तविक है

$⇒  ad + bc = 0$ 

$⇒ a( – b) + bc = 0 ⇒ a = c$

${z_1} = a + ib = c – id = {\bar z_2}$ $(\because a = c$ एवं $b =  – d)$

Standard 11
Mathematics

Similar Questions

Start a Free Trial Now

Confusing about what to choose? Our team will schedule a demo shortly.