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blagie [28]
3 years ago
7

Why does the multiplicative inverse of a number have the same sign as the number?

Mathematics
1 answer:
denis23 [38]3 years ago
7 0
<span>Look at the definition of multiplicative inverse. If two numbers are multiplicative inverses of each other, then by definition, their product will be equal to 1. And 1 is a positive number. If both numbers being multiplied are positive, then the result is positive. And of both numbers being multiplied are negative, then the result is still positive. But if one number is positive and the other is negative, then the result is negative. So if you want a positive result, then both numbers you're multiplying have to have the same sign. And since we want a result of 1 for multiplicative inverses and since 1 is positive, then the numbers being multiplied have to have the same sign.</span>
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Answer:

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Step-by-step explanation:

-sqrt(3) -i

We can find the radius

r = sqrt( (-sqrt(3)) ^2 + (-1) ^2)

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theta = arctan (y/x)

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theta = pi/6

But this is in the first quadrant, and we need it in the third quadrant

Add pi to move it to the third quadrant

theta = pi/6 + 6pi/6

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-sqrt(3) -i = 2 cis (7pi/6)

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