Transcription of Week 4 – Complex Numbers
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Week 4 – Complex Numbers
Week 4 Complex Numbers Richard Earl . Mathematical Institute, Oxford, OX1 2LB, November 2003. Abstract cartesian and polar form of a Complex number . The Argand diagram. Roots of unity. The relation- ship between exponential and trigonometric functions. The geometry of the Argand diagram. 1 The Need For Complex Numbers All of you will know that the two roots of the quadratic equation ax2 + bx + c = 0 are . b b2 4ac x= (1). 2a and solving quadratic equations is something that mathematicians have been able to do since the time of the Babylonians. When b2 4ac > 0 then these two roots are real and distinct; graphically they are where the curve y = ax2 + bx + c cuts the x-axis. When b2 4ac = 0 then we have one real root and the curve just touches the x-axis here.
Week 4 – Complex Numbers Richard Earl ∗ Mathematical Institute, Oxford, OX1 2LB, November 2003 Abstract Cartesian and polar form of a complex number. The Argand diagram. Roots of unity. The relation-ship between exponential and trigonometric functions. The geometry of the Argand diagram. 1 The Need For Complex Numbers
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