Q10 of 202 Page 188

For all z C, prove that

(i)


(ii) .


(iii) = |z|2


(iv) is real


(v) is 0 or imaginary.


Let z = a + ib



Hence Proved.


(ii) Let z = a + ib






Hence, Proved.


(iii) Let z = a + ib




Hence Proved.


(iv) Let z = a + ib




Hence , is real.


(v) Case 1. Let z = a + 0i




Case 2. Let z = 0 + bi




Case 2. Let z = a + ib




Thus, is 0 or imaginary.


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