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Let z* denote the conjugate of the complex number z, that is, (a + bi)* = a - bi. Prove

Chapter 32, Problem 32.16

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QUESTION:

Let z* denote the conjugate of the complex number z, that is, (a + bi)* = a - bi. Prove thateach of the following is true for each z E C.(a) (z*)* = z (b) z + z* E lR(c) z = z* iff Z E lR (d) (Z-I)* = (Z*)-I

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QUESTION:

Let z* denote the conjugate of the complex number z, that is, (a + bi)* = a - bi. Prove thateach of the following is true for each z E C.(a) (z*)* = z (b) z + z* E lR(c) z = z* iff Z E lR (d) (Z-I)* = (Z*)-I

ANSWER:

Step 1 of 5

Given  denotes the conjugate of the complex number z

a) If  

                       

                               

                               

                               

 

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