1.

Show thatRe(z_1z_2)=Rez_1Rez_2-Im z_1Imz_2Im(z_1z_2)=Re z_1 Im z_2+Re z_2 Im z_1

Answer»

SOLUTION :LET `z_1=a+ib,z_2=c+id`
`:. z_1z_2=(a+ib),(c+id)`
`=ac+iad+ibc+i^2bc`
`=(ac-bd)+i(ad+bc)`
`:."Re"(z_1z_2)=ac-bd="Re"z_1."Re"z_2-"IM" z_1."Im"z_2`
`"Again,Im"z_1z_2=ad+bc="Re" z_1."Im"z_2,"Re"z_2`


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