2 years ago

Find the magnitude and direction of r+u please help !!

Mathematics

1 answer:

solniwko [45]2 years ago

3 0

Answer:

5.4 cm; 133 degrees

Step-by-step explanation:

hope this helps

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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

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Here, a=0 and b=-5. $\theta$ lies in 4th quadrant.

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

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

$\tan \theta=\infty$

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

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

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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Step-by-step explanation:

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