Question 5 [20 marks]. Suppose

A

and

B

are sets for which\

|A|=6,|B|=7,|A\\\\cap B|=3.

\ (a) Write down the number of 2-element subsets of

B

.\ (b) Find

|A\\\\cup B|

. Justify your answer briefly.\ (c) Let

D={CinP(A):|C\\\\cap B|=1}

. Find

|D|

. Justify your answer, using any results you need\ from lectures.\ (d) Let

z

be the complex number

1+3

i. Find the following. [You do not need to show your\ working, but doing so may help you to gain marks if you make arithmetic errors.]\ (i)

z^(2)

.\ (ii)

|z|^(2)

.\ (iii) A complex number

w

such that

z-w

and

zw

are both real numbers.

Question 5 [20 marks]. Suppose A and B are sets for which A=6,B=7,AB=3. (a) Write down the number of 2-element subsets of B. (b) Find AB. Justify your answer briefly. (c) Let D={CP(A):CB=1}. Find D. Justify your answer, using any results you need from lectures. (d) Let z be the complex number 1+3 i. Find the following. [You do not need to show your working, but doing so may help you to gain marks if you make arithmetic errors.] (i) z2. (ii) z2. [3] (iii) A complex number w such that zw and zw are both real numbers. [4]