Creelman Exam Questions. [10 marks] 12:CA15 3. (a) Sketch the following regions in the complex plane. (ii) Im z 2 2 Rez - 1 (1) 1z- 3+4i1 57 12- (3- 43) 137 Im(z) Im(z) 5+ N Re(z 3- 2 - 1 2 3 4 5 6 7 8 9 10 11 12 13 8 -7 6 -5 4 32-13 Re( 2 ) OUT A W N -7+ 8- -10 -11- (b) The set of points in the complex plane that satisfy (z - 3 -i) = [z -a - bil, where a and b are certain real constants, can alternatively be defined by the property that they lie on the line Im z = -2 Rez + 17. Determine the values of a and b. 12- ( 3+1) 1 = 12- ( atbill y = - 2x+17 [4] ( #- 3 ) + ( 4 +1 )? = ( x - a )? + (y +b )?Creelman Exam Questions. [10 marks] 12:CA15 3. (a) Sketch the following regions in the complex plane. (ii) Im z 2 2 Rez - 1 (1) 1z- 3+4i1 57 12- (3- 43) 137 Im(z) Im(z) 5+ N Re(z 3- 2 - 1 2 3 4 5 6 7 8 9 10 11 12 13 8 -7 6 -5 4 32-13 Re( 2 ) OUT A W N -7+ 8- -10 -11- (b) The set of points in the complex plane that satisfy (z - 3 -i) = [z -a - bil, where a and b are certain real constants, can alternatively be defined by the property that they lie on the line Im z = -2 Rez + 17. Determine the values of a and b. 12- ( 3+1) 1 = 12- ( atbill y = - 2x+17 [4] ( #- 3 ) + ( 4 +1 )? = ( x - a )? + (y +b )