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COMPLEX JEAPORDY

COMPLEX JEAPORDY. 10. 10. 10. 10. 2 0. 2 0. 2 0. 2 0. 30. 30. 30. 30. 10 0. 10 0. 10 0. 50. 10 points. Log Rules. Write as the log of a single number: 3log(5)+2log(3)-log(5). log225. 20 points. Exponential Equations. Solve 2 3x-1 =12. X=1.528. 30 points. Log equation.

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COMPLEX JEAPORDY

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  1. COMPLEX JEAPORDY 10 10 10 10 20 20 20 20 30 30 30 30 100 100 100 50

  2. 10 points. Log Rules • Write as the log of a single number: • 3log(5)+2log(3)-log(5) log225

  3. 20 points. Exponential Equations • Solve 23x-1=12 X=1.528

  4. 30 points. Log equation • Solve ln(x+3)=ln(x)+ln(3) X=3/2 or 1.5

  5. 50 points. Solving with logs • Solve this for x in terms of k

  6. 10 points. Argand Diagrams, manipulation • What are the complex numbers a and c ? • Find ac where a and c are shown below: A=(1+2i) C=(-3+4i) AC=(-11-2i)

  7. 20 points. Modulus • Find the modulus of z where z=2+3i [z]=√13

  8. 30 points. Imaginary factors is a root of Find the value of A A=6

  9. 10 points. Simplify

  10. 20 points. Rationalise the denominator

  11. 30 points. Irrational Equation • Solve: X=8 (x=1 does not hold)

  12. 100 points. Harder solving • Solve the equation X=19.6 or 1.38

  13. 10 points. Use the factor theorem to factorise & hence solve (x-1)(x+2)(x+5)=0 X=1,-2 or -5

  14. 20 points. Solve the following equation by completing the square

  15. 30 points. Solving • One root of the equation is 2i. • Find the value of k and the two remaining roots. • f(2i)=0 since 2i is a root. By substitution (factor theorem) k must equal 32. • Roots are 2i, -2i (conjugate root theorem) and -8 (by evaluating constant)

  16. 100 points. Binomial Expansion Find the value of the term that is independent of x (the constant) in the expansion of: For r=8, the (9th) term is:

  17. 100 points. Algebraic Proof • Show that if w and z are two complex numbers. • Let w=x+yi and z=a+ib • LHS: (x-yi)(a+bi)=ax+bxi-ayi-byi2=ax+by+bxi-ayi=ax+by+(bx-ay)i • RHS: =LHS Therefore statement is true

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