COMPLEX NUMBERS AND VECTORS
C O N T E N T S COMPLEX NUMBERS AND VECTORS IN THE SECONDARY CURRICULUM INTRODUCTION COMPLEX NUMBERS A TALE OF INTRIGUE AND IMAGINATION THINKING OUTSIDE THE SQUARE ALL IS NUMBER INTRIGUE AND 2 SECRECY, CONTRIVANCE AND INSPIRATION RENAISSANCE ITALY AND MATHEMATICAL DUELS TWO NEGATIVES MAKE A POSITIVE # - - = ^ H QUADRATIC EQUATIONS AND THE CARTESIAN PLANE FORM AND STRUCTURE: A CAREFUL EXPOSITION ON OPERATING WITH COMPLEX NUMBERS ADDITION SUBTRACTION MULTIPLICATION POLAR COORDINATES DIVISION THE GENIUS OF GAUSS THE FUNDAMENTAL THEOREM OF ALGEBRA CONJUGATE ROOT THEOREM THE FUNDAMENTAL THEOREM OF ARITHMETIC MATHEMATICIANS CAN READ MAPS FUNCTIONS OF A REAL VARIABLE FUNCTIONS OF A COMPLEX VARIABLE MAPPING FUNCTIONS OF A COMPLEX VARIABLE THE FUNCTION F Z EZ = ] G INTERSECTING TANGENTS SETS, CURVES AND REGIONS (WHO ARE OUR NEIGHBOURS?) PLOTTING A COURSE SEEING THROUGH THE FOG ANCIENT NAVIGATION AND VECTORS SINKING THE SPANISH ARMADA AND VECTORS SAILING AGAINST THE WIND TACKING INTO THE WIND THE SCALAR OR DOT PRODUCT OF TWO VECTORS PERPENDICULAR VECTORS DIRECTION COSINES OF A VECTOR PARALLEL AND PERPENDICULAR COMPONENTS FOR P~ THE CROSS PRODUCT OF TWO VECTORS VECTOR COMPONENTS AND THE CROSS PRODUCT MEASURING TORQUE MULTIPLYING VECTORS THREE AT A TIME VOLUME OF A PARALLELEPIPED IT’S A CIRCUS PLOTTING A PATH FINDING CARTESIAN EQUATIONS FROM PARAMETRIC EQUATIONS VECTOR CALCULUS SUPPORTING CIRCUS PERFORMERS MATHEMATICS AND THE HUMAN CANNONBALL BAREBACK HORSE RIDING 10 IT’S NOW POSSIBLE TO KNOW WHERE WE ARE! THE IMPORTANCE OF KNOWING WHERE YOU ARE WORKING OUT YOUR LOCATION VECTORS AND VECTOR OPERATIONS USING MATRICES LINEAR COMBINATION OF VECTORS TRANSPOSITION OF VECTORS USING MATRIX MULTIPLICATION SOLVING SIMULTANEOUS EQUATIONS MATHEMATICS AND THE LOCATION OF EARTHQUAKES 11 PONS ASINORUM—THE ASSES’ BRIDGE VECTOR PROOFS USING THE SCALAR PRODUCT 12 CURRICULUM CONNECTIONS 13 SOLUTION NOTES TO STUDENT ACTIVITIES REFERENCES AND FURTHER READING