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djyliett [7]
3 years ago
8

When you multiply two complex numbers in polar form, what happens to the angles?

Mathematics
1 answer:
prisoha [69]3 years ago
6 0

The angles get added.

Let <em>z</em> = <em>r</em> exp(<em>i</em> <em>θ</em>) and <em>w</em> = <em>s</em> exp(<em>i</em> <em>φ</em>). Then

<em>zw</em> = <em>rs</em> exp(<em>i</em> <em>θ</em>) exp(<em>i</em> <em>φ</em>) = <em>rs</em> exp(<em>i</em> (<em>θ</em> + <em>φ</em>))

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Step-by-step explanation:

In mathematics, a cube root of a number x is a number y such that y³ = x. All nonzero real numbers, have exactly one real cube root and a pair of complex conjugate cube roots, and all nonzero complex numbers have three distinct complex cube roots. For example, the real cube root of 8, denoted ³√8, is 2, because 2³ = 8, while the other cube roots of 8 are −1 + √3i and −1 − √3i. The three cube roots of −27i are 3i, 3√(3)/2-3/2i, and -3√(3)/2-3/2i.

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Answer:

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Step-by-step explanation:

Expand the following:

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3 4 x^2 x^2 + 18 x^3 - 9 x^2

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Answer:  12 x^4 + 18 x^3 - 9 x^2

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