18 - 24i write in trigonometric form

Mathematics

1 answer:

stiks02 [169]3 years ago

6 0

$\boxed{18-24i=30(cos(5.36)+isin(5.36))}$

<h2>Explanation:</h2>

Unlike 0, we can write any complex number in the trigonometric form:

$z=r(cos\alpha+isin\alpha)$

We have the complex number:

$18-24i$

So $r$ can be found as:

$r=\sqrt{x^2+y^2} \\ \\ \\ Where: \\ \\ x=18 \\ \\ y=-24 \\ \\ r=\sqrt{18^2+(-24)^2} \\ \\ r=\sqrt{324+576} \\ \\ r=\sqrt{900} \\ \\ r=30$

Now for α:

$\alpha=arctan(\frac{y}{x}) \\ \\ Since \ the \ complex \ number \ lies \ on \ the \ fourth \ quadrant: \\ \\ \alpha=arctan(\frac{-24}{18})=-53.13^{\circ} \ or \ 360-53.13=306.87^{\circ}$

Finally:

$Convert \ into \ radian: \\ \\ 360^{\circ}\times \frac{\pi}{180}=5.36rad \\ \\ \\ Hence: \\ \\ \boxed{18-24i=30(cos(5.36)+isin(5.36))}$

<h2>Learn more:</h2>

Complex conjugate: brainly.com/question/2137496

#LearnWithBrainly

You might be interested in

Formula for a prism i am in need of help please help me

LenaWriter [7]

V=1/2a*c*h this is to solve the volume of a prism

4 0

3 years ago

For circle O, mCD=125° and m

Burka [1]

CA is a diameter of the circle, so $m\widehat{AC}=180^\circ$ , which means $m\angle AOB=m\angle AOD=m\widehat{AD}=180^\circ-m\widehat{CD}=55^\circ$ . Then $m\boxed{\angle ABO}=90^\circ-55^\circ=35^\circ$ .

This means $m\angle CBO=55^\circ-35^\circ=20^\circ$ . Also, if $m\angle AOB=55^\circ$ , then $m\angle BOC=180^\circ-55^\circ=125^\circ$ , which in turns tells us that $m\boxed{\angle BCO}=180^\circ-20^\circ-125^\circ=35^\circ$ .