Investigation

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Submitted By KhuanChinn
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TUTORIAL 1 NUMBER AND SET

1.1 Exponential and Logarithm Equations

1. Evaluate each expression (a) [pic] (b) [pic] (c) [pic]

2. Solve the following exponential equations.

(a) [pic] (b) [pic]

(c) [pic]

3. Solve each of the following equations.

(a) [pic] (b) [pic]

(c) [pic]

4. Solve the logarithmic equations for [pic]

(a) [pic] (b) [pic]

(c) [pic]

5. Solve the following equations: (i) [pic] (ii) 32x+ 2 – 28 (3x) + 3 = 0 (iii) [pic] (iv) [pic] (v) [pic]

6. Solve the following equations: (i) [pic] (ii) log2 x + 3logx 2 = 4 (iii) [pic] (iv) [pic] (v) [pic]

7. Solve the following simultaneous equations: (i) [pic] [pic]

(ii) [pic] [pic]

(iii) [pic] [pic]

8. Find the smallest positive integer n such that (i) [pic] (ii) [pic] (iii) [pic]

9. (a) If[pic], prove that[pic]. (b) Given [pic]solve for x.

1.2 Complex Numbers

10. Evaluate the expression and write the result in the form [pic]

(a) [pic] (b) [pic]

(c) [pic] (d) [pic]

(e) [pic] (f) [pic]

(g) [pic] (h) [pic]

11. Given that [pic], find the values of p and q.

12. Find [pic] in the form [pic], where [pic]

13. If [pic] and [pic], find

(a) [pic] [pic] (b) [pic] [pic]

14. Solve the following equation for the values of x and y:

[pic]

15. Express the following complex numbers in the form a + bi. (i) [pic] (ii) [pic] (iii) [pic] (iv) [pic] (v) [pic] (vi) [pic] (vii) [pic] (viii) [pic] (ix) [pic] (x) [pic] (xi) [pic] (xii) [pic]

16. Express z = [pic] in the form x + yi, where x and y are real numbers. Draw an Argand diagram to show the location of z. Hence, find the modulus and argument of z.

17. Find the value of x and y, [pic], for the…...

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