Exercise 2.3: Properties of Complex Numbers

EXERCISE 2.3

1. If z1 = 1- 3i, z2 = -4i , and z3 = 5 , show that

(i) ( z1 + z2 ) + z3  = z1 + ( z2 + z3)

(ii) ( z1z2) z3 = z1 ( z2 z3 )

2. If z1 = 3, z2 = -7i, and z3 = 5 + 4i , show that

(i) z1 (z2 + z3 ) = z1 z2  + z1 z3

(ii) (z1 + z2 )z3 = z1 z3 + z2 z3 .

3. If z1 = 2 + 5i, z2 = -3 - 4i, and z3 = 1+ i , find the additive and multiplicative inverse of z1 , z2 , and z3.

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