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Argand diagram inquiry

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On an Argand diagram a complex number and its reciprocal are perpendicular.

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On an Argand diagram a complex number and its reciprocal are perpendicular.

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Think Pair – Share

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On an Argand diagram a complex number and its reciprocal are perpendicular.

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Reciprocal

Several numbers are shown on the Argand diagram.

The circle has a radius 1 and centre at the origin.

Which of these numbers is the reciprocal of F?

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Generalisation

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Complex number

Modulus

Argument

Reciprocal

Modulus

Argument

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Complex number

Modulus

Argument

Reciprocal

Modulus

Argument

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Generalisations

The modulus of the reciprocal is ……

The argument of the reciprocal is ……

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Proof of the general case

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