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kupik [55]
3 years ago
11

Pls tell me the answer with the work shown

Mathematics
1 answer:
shepuryov [24]3 years ago
4 0

Answer:

plug in the numbers for radius, and know your formulas. a diameter is 2 times a radius so

Pi or 3.14 times D is the same as 2 times pi times radius.

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WILL GIVE BRAINLEST ANSWER IF ANSWERED IN THE NEXT 24 HRS Express the complex number in trigonometric form. -5i
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Answer:

z=5\left(\cos \left(\dfrac{3\pi}{2}\right)+i\sin \left(\dfrac{3\pi}{2}\right)\right)

Step-by-step explanation:

If a complex number is z=a+ib, then the trigonometric form of complex number is

z=r(\cos \theta +i\sin \theta)

where, r=\sqrt{a^2+b^2} and \tan \theta=\dfrac{b}{a}, \theta is called the argument of z, 0\leq \theta\leq 2\pi.

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It can be rewritten as

z=0-5i

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r=\sqrt{0^2+(-5)^2}=5

\tan \theta=\dfrac{-5}{0}

\tan \theta=\infty

\theta=2\pi -\dfrac{\pi}{2}    [\because \text{In 4th quadrant }\theta=2\pi-\theta]

\theta=\dfrac{3\pi}{2}

So, the trigonometric form is

z=5\left(\cos \left(\dfrac{3\pi}{2}\right)+i\sin \left(\dfrac{3\pi}{2}\right)\right)

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