If (w) and (z) are complex numbers then show that w−z¯=w¯−z¯

Expert Solution & Answer

Explanation of Solution

Given information: The given complex numbers are (w) and (z) .

Proof: Consider that w=w1+iw2 and z=z1+iz2 where w1,w2,z1 and z2 belongs to real numbers. Now evaluate w−z¯ with the help of w=w1+iw2 and z=z1+iz2 .

w−z=(w1+iw2)−(z1+iz2)w−z=(w1−z1)+i(w2−z2)w−z¯=(w1−z1)+i(w2−z2)¯....(Conjugate)w−z¯=(w1−z1)−i(w2−z2) ....(1)

Similarly evaluate w¯+z¯ ,

w¯−z¯=(w1+iw2)¯−(z1+iz2)¯w¯−z¯=(w1−iw2)−(z1−iz2)w¯−z¯=(w1−z1)−i(w2−z2) ....(2)

Hence combined (1) and (2) it is proved that w−z¯=w¯−z¯ .

Chapter 6.8, Problem 16E

Chapter 6.8, Problem 18E

Chapter 6 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

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