Question

How do you multiply `(5-12i)(2+3i)` in trigonometric form?

Answer 1

`=46-19i`

Explanation:

Expanding these factors is determined by applying Distributive property.
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Distributive Property:
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`color(blue)((a+b)(c+d) = axxc + axxd + bxxc + bxxd)`
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`(5 - 12i)(2 + 3i)`
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`=color(blue)(5xx2 + 5xx3i +(-12i)xx2 + (-12ixx3i))`
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`=10 + 5i -24i -36i^2`
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`=10 -19i-36xx-1" "`As we know `" "i^2=-1`
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`=10-19i+36`
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`=46-19i`