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Are you ready for more On October 16 1843 while walking across the Broom Bridge...

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Algebra

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Are you ready for more On October 16 1843 while walking across the Broom Bridge in Dublin Ireland Sir William Rowan Hamilton came up with an idea for numbers that would work sort of like complex numbers Instead of just the number i and its opposite i squaring to give 1 he imagined three numbers i j and k each with an opposite that squared to give 1 The way these numbers multiplied with each other was very interesting i times j would give k j times k would give i and k times i would give j But the multiplication he imagined did not have a commutative property When those numbers were multiplied in the opposite order they d give the opposite number So j times i would give k k times j would give i and i times k would give j A quaternion is a number that can be written in the form a bi cj dk where a b c and d are real numbers Let w 2 3i jand z 2i 3k Write each given expression in the form a bi cj dk 1 w z 2 Wz

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