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 agoShow that 1 + i^{10} + i^{20} + i^{30} is a real number?

Solve the quadratic equations by factorization method only 6x^{2} – 17ix – 12 = 0

Solve the quadratic equations by factorization method only x^{2} + (1 – 2i)x – 2i = 0

Solve the quadratic equations by factorization method only x^{2} + 10ix – 21 = 0

Solve the quadratic equations by factorization method only 17x^{2} – 8x + 1 = 0