5. Let 2₁ and 22 be complex numbers. In particular, let z₁ = a + bi and 22 = c + di, wherea, b, c, d are real numbers.(a) Show that the conjugate of the sum of 2₁ and 22 is the same as the sum of theirconjugates. That is, show that21 +2₂=2₁ +22(b) Show that the conjugate of the product of 2₁ and 2₂ is the same as the product of theirconjugates. That is, show that21 22 21 22Note: It is mathematically poor form to work two sides of an equation at once. You canstart on one side and work your way to the other, or work both sides separately and showthat your separate calculations give the same result.

Given: z1=a+biz2=c+di We are required to prove a. z1+z2=z1+z2b. z1.z2=z1.z2

Let 21 and 22 be complex numbers. In particular, let z₁ = a + bi and 22 = c + di, where a, b, c, d are real numbers. (a) Show that the conjugate of the sum of 2₁ and 22 is the same as the sum of their conjugates. That is, show that 21+22= 21+%2 (b) Show that the conjugate of the product of 2₁ and 22 is the same as the product of their conjugates. That is, show that 21 22 = 21 22 .