(a) Simplify the following:

Question

(i) i345
(ii) 32/(-5i)
(iii) 6/(7-8i)
(iv) 9/(-8+7i)

(b) Find the nature of the stationary points on the curve y = 4x3 – 3x2 – 6x + 2

Answer 1

a. 1. i345 = 345i.

2. 32/-5i = 32*5i/(5i*5i) = 160i/25i^2 = 160i/-25.

3. 6/(7-8i) = 6*(7+8i)/(7-8i)(7+8i) = 42+48i/(49+56i-56i-64i^2) = 42+48i/(49+64) = 42+48i/113.

4. 9/(-8+7i). Use same procedure as part 3 and remember that i^2 = -1.