Q2 of 202 Page 188

Express each of the following in the form (a + ib) and find its multiplicative inverse:

(i)


(ii)


(iii)


(i) Let






∴ the multiplicative inverse of



(ii) Let





z = - 1 + i



⇒ |z|2 = ( - 1)2 + (1)2 = 1 + 1 = 2


∴ the multiplicative inverse of



(iii) Let





Z = - 1 + i√3



⇒ |z|2 = ( - 1)2 + (√3)2 = 1 + 3 = 4


∴ the multiplicative inverse of



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28

Find the complex number z for which |z| = z + 1 + 2i.

 1

Express each of the following in the form (a + ib) and find its conjugate.

(i)


(ii) (2 + 3i)2


(iii)


(iv)


(v)


(vi)


3

If (x + iy)3 = (u + iv) then prove that = 4 (x2 – y2).

 4

If (x + iy)1/3 = (a + ib) then prove that = 4 (a2 – b2).