658 prompts matching "Explain why a complex number times its conjugate is real"
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Common Mistakes: Expanding the product of two surd brackets
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Spot My Mistake: Rationalising and then cancelling a common factor
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Show All Working: Checking a rationalised answer by decimal approximation
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Common Mistakes: Rationalising a denominator of the form root a over root b
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Final Revision: Expressing a rationalised answer in the form a root b over c
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Practice: Rationalising a denominator of the form a plus root b over c minus root d
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Common Mistakes: Rationalising when both terms of the denominator are surds
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Common Mistakes: A surd equation that has no real solution
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Learn: What a binary operation actually is
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Explain Back: A binary operation defined on the integers
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Common Mistakes: A binary operation that is ordinary addition in disguise
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Final Revision: Deciding whether a given rule really is a binary operation
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Show All Working: Showing a set is not closed by a single counter-example
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Common Mistakes: Closure on a set of three elements under a stated rule
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Practice: An operation that is not commutative, with a counter-example
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Explain Back: What it means for an operation to be associative
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Show All Working: An operation that is associative but not commutative
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Common Mistakes: Subtraction as an example of neither law
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Learn: What it means for one operation to distribute over another
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Practice: Multiplication distributing over addition in ordinary arithmetic
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