Question

plz answer me this question

Answer 1

   solution

given that  z₁=2+3i  and  z₂=1-i

then to show that |z₁||z₂|=|z₁z₂|

|z₁|=√2²+3²  =√4+9  =√13

|z₂|=√1²+(-1)²  =√1+1  =√2

⇒|z₁||z₂|=√13*2 =√26

i:e |z₂*z₂|=√5²+(-1)²  =√25+1  =√26

⇒|z₁|*|z₂|=|z₁*z₂|

note: z*z₂=(2+i)(1-i)

=2-2i+31-3i²  =2-i+3

⇒|z₁*z₂|=|z₁||z₂|