NEED HELP ! 20 POINTS

Mathematics

1 answer:

prohojiy [21]3 years ago

8 0

If $z=1-i$ , then $|z|=\sqrt{1^2+(-1)^2}=\sqrt2$ and $\arg z=-\dfrac\pi4$ because $z$ lies in the fourth quadrant.

By DeMoivre's theorem,

$z=|z|e^{i\arg z}\implies z^{10}=(\sqrt2)^{10}e^{-i10\pi/4}=32e^{-i5\pi/2}=32e^{-i\pi/2}=-32i$

so the answer is B.

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Find the smallest number that divides by 44 55 and 220 leaving remainder 5

galina1969 [7]

The numbers from which we are to determine the smallest number that can be divided leaving a remainder of 5 are 44, 55, and 220. We have to do the prime factorization of all the numbers to determine their least common multiple (LCM).

Factorization of 44:
44 = 11 x 4 = 11 x 2 x 2

Factorization of 55:
55 = 11 x 5

Factorization of 220:
220 = 11 x 20 = 11 x 5 x 4

Since 220 has all the factors from 55 and 44 then, the least common multiple is 220. Add 5 to the LCM in order to determine the unknown.

ANSWER: 225

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