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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 |
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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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