For any two complex numbers z1 and z2, prove that Re (z1z2) = Re zRe z2 – Im z1 Im z2

Asked by Pragya Singh | 1 year ago |  110

1 Answer

Solution :-

Let = \( z_1=x_1+iy_1\) and \( z_2=x_1+iy_2\)

\( z_1z_2=(x_1+iy_1)(x_2+iy_2)\)

\( x_1(x_2+iy_2)+iy_1(x_2+iy_2)\)

\( x_1x_2+ix_1iy_2+iy_1x_2+i^2y_1y_2\)

\( x_1x_2+ix_1y_2+iy_1x_2-y_1y_2\)

\( (x_1x_2-y_1y_2)+i(x_1y_2+y_1x_2)\)

\( Re(z_1z_2)=x_1x_2-y_1y_2\)

\( Re(z_1z_2)= Rez_1 Rez_2-Imz_1 Imz_2\)

Hence, proved

Answered by Abhisek | 1 year ago

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