Question

11th complex number miscellaneous exercise solution question number question no 2 1)2)​

Answer 1

Hi mate here is your answer:--

Step-by-step explanation:

Question 2 miscellaneous-

For any two complex numbers z1 and z2, prove that

Re (z1 z2) = Re z1 Re z2 – Imz1 IMz2

Answer:-

It is given in question that z1 and z2 are complex number and we have to prove that,

Re (z1z2) = Rez1 Rez2 – Imz1 Imz2

so , firstly let

z1 = x1 + iy1 and z2 = x2 + iy2

Thus, z1z2 = (x1 + iy1) (x2 + iy2)

=x1 (x2 + iy2) + iy1 (x2 + iy2)

= x1x2 + ix2y2 + iy1x2 + i2y1y2

= x1x2 + ix2y2 + iy1x2 – y1y2 (i2 = - 1)

= (x1x2 – y1y2) + i (x1y2 + y1x2)

= Re (z1z2) = x1x2 – y1y2

∴ Re (z1z2) = Rez1 Rez2 – Imz1 Imz2

Hence, proved

Hope it helps you ❣️