Question

02. (2). If |2-3|=|z+il. (1). Use an algebraic method to find a Cartesian equation of the locus of 2 (11) Sketch the locus of zon an Argand diagram. (6). If are 9- (1). Sketch the locus of P(x,y) which is represented by z on an Argand diagram (i). Find the Cartesian equation of this locus. (c). Given that the complex number z=x+iy where x,y e Rssatisfies the equation 12-12-51 = 3, find the minimum value and the maximum value of -1. (d). (1). Using De Moivre's theorem and the binomial theorem, show that cos 48 = cos - 6 cos sin +sino sin 40 = 4 cos sin 8-4cos sin (11) Find all the values of 8". (a). A husband and wife participate in an interview for two vacancies in the same post. The probability that thehusband will be selected is 1/7 and that of wife is 1/5. What is the probability that 1). Both of them will be selected. (11). Only one of them will be selected. (iii). None of them will be selected. (b). State and Prove Baye's Theorem. A diagnostic test has a probability 0.95 of giving a positive result when applied to a person suffering from a certain disease, and a probability 0.10 of giving a (false) positive when applied to a non-sufferer. It is estimated that 0.5% of the population are sufferers. Suppose that the test is now administered to a person about whom we have no relevant information relating to the disease (apart from the fact that he she comes from this population). Calculate the following probabilities:

Answer 1

- 2) a) (1) 12-3)=|ztil z=xtiya :: petiy-31= 1xtinti / ) Ja-3)?+32 -7546341Z x² - 6x + 9 +2= x+2y tity? = 6x +2y = 8 :. 32+y = 4 In cartesian egnation locus of z is 38+524 wrich is a s straight " 3at you CZ-2) \324yry Who) ay ( 2-4 ) = 1/4. - arg (2-6) -arg (2-2) - My o o non 2-6= xotiy -6 = x-6 try :-org (2-6)=tant(y) - z-2= atiy-2 =2- 2tiy-arg (2-2) = tout y bobl :. =) taño tant ( 17 ) = 7 a) taño a la loro le ore )anu 1 to be on J : tarify (an2-x+6) ja ty x²_88412 + y2 1. 4 y al 22 1 x 8x+7+12 - 82+12+ 42-44 =0 5) 22-2..4 +16 +42_2.4.2 +4 = 8 -) (24-4)3 +(y-2) = (202) circle, with radii 2.2, centre This is a equation of at (4,2). () Loens of poly): circle. 3 (1) Equations. (-4) ²70-273 = (252) 2

010), 10) 12-126-511 9. ..? 5) 124-12 tily-52), 39 - lume siste 112.)? Hi-5)?-a la-12) +(3-5)= 9 . This is a circle with centra l at (12,5) and radii = 3: Now the distance from (oro) to (12,5) 1 viuutiso = VT 69=13 #1 Maşimum distame from (ao) to the on the circle = 13t rädins = 13+3=16 and Minimum distance froom (oo) to the on circle - 13- rading - 13-3 210 Mininum valine of 121=10 Marimum in I216016.. Another wayo point point ||22217,112,1-17211 :.35|2 - {zxsil 7,1121 – 12+507 1 =712) -131 :: 121-13 153 18=13-3</21 < 13+3=16 . Madimum of 121= 16. & Minimum of 121 = 10