1,331 prompts matching "Teach me dividing complex numbers by rationalising with the conjugate"
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Final revision: my three hardest Further Maths topics
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Worked Example: The intersection of two overlapping sets
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Practice: The difference of two sets, A minus B
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Common Mistakes: Showing that intersection distributes over union
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Worked Example: Testing whether a binary operation is closed on a given set
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Practice: Testing a binary operation for associativity
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Worked Example: Collecting like surds in a single sum
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Common Mistakes: Solving an equation in which the unknown sits under a root
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Worked Example: Simplifying an expression carrying both a negative and a fractional index
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Practice: Converting between index form and logarithm form
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Explain Back: The laws of logarithms for a product and for a quotient
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Common Mistakes: Solving an exponential equation using logarithms
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Practice: The condition for a quadratic equation to have equal roots
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Explain Back: The range of values of k for which the roots are real
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Common Mistakes: Proving that a quadratic expression is positive for every real x
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Worked Example: Finding one over alpha plus one over beta
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Practice: Finding alpha minus beta from the sum and the product
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Explain Back: Finding alpha squared beta plus alpha beta squared
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Practice: Factorising a cubic completely once one factor is known
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Explain Back: Finding an unknown coefficient given that a stated factor divides the polynomial
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