Question

Question 2 For any two complex numbers z1 and z2, prove that

Re (z1z2) = Re z1 Re z2 – Im z1 Im z2

Class X1 - Maths -Complex Numbers and Quadratic Equations Page 112

Answer 1

Re(z1.z2) = Re(z1).Re(z2)- Im(z1).Im(z2)

concept :-
If z = a + ib , then
a is known as real part of complex number and denoted by Re(z) . similarly b is known as imaginary part of complex number and denoted by Im(z)

solution:-
Let z1 = a + ib
Then, Re(z1) = a -----(1)
Im(z1) = b--------(2)

Let z2 = c + id
Then, Re(z2) = c--------(3)
Im(z2) = d-----------(4)
Now,
z1.z2 = (a+ib)(c+id)
= ac + iad + icd + i²bd
= ac + i(ad +cd) -bd
= (ac - bd) + i(ad + cd)

Re(z1.z2) = ac - bd
From eqns (1), (2), (3) and (4)
Re(z1.z2) = Re(z1).Re(z2) - Im(z1).Im(z2)

Answer 2

Step-by-step explanation:

it can be solved by using this method and hoping it will make you understand easily ....

thanks