Question

|z1-z2|^2 = |z1|^2 + |z2|^2 prove that​

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)

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Answer 2

Step-by-step explanation:

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