Answer:
Solution : 6 + 6i
Step-by-step explanation:
![-3\left[\cos \left(\frac{-\pi }{4})\right+i\sin \left(\frac{-\pi }{4}\right)\right]\cdot \:2\sqrt{2}\left[\cos \left(\frac{-\pi }{2}\right)+i\sin \left(\frac{-\pi }{2}\right)\right]](https://tex.z-dn.net/?f=-3%5Cleft%5B%5Ccos%20%5Cleft%28%5Cfrac%7B-%5Cpi%20%7D%7B4%7D%29%5Cright%2Bi%5Csin%20%5Cleft%28%5Cfrac%7B-%5Cpi%20%7D%7B4%7D%5Cright%29%5Cright%5D%5Ccdot%20%5C%3A2%5Csqrt%7B2%7D%5Cleft%5B%5Ccos%20%5Cleft%28%5Cfrac%7B-%5Cpi%20%7D%7B2%7D%5Cright%29%2Bi%5Csin%20%5Cleft%28%5Cfrac%7B-%5Cpi%20%7D%7B2%7D%5Cright%29%5Cright%5D)
This is the expression we have to solve for. Now normally we could directly apply trivial identities and convert this into standard complex form, but as the expression is too large, it would be easier to convert into trigonometric form first ----- ( 1 )
( Multiply both expressions )
![-6\sqrt{2}\left[\cos \left(\frac{-\pi }{4}+\frac{-\pi \:\:\:}{2}\right)+i\sin \left(\frac{-\pi \:}{4}+\frac{-\pi \:\:}{2}\right)\right]](https://tex.z-dn.net/?f=-6%5Csqrt%7B2%7D%5Cleft%5B%5Ccos%20%5Cleft%28%5Cfrac%7B-%5Cpi%20%7D%7B4%7D%2B%5Cfrac%7B-%5Cpi%20%5C%3A%5C%3A%5C%3A%7D%7B2%7D%5Cright%29%2Bi%5Csin%20%5Cleft%28%5Cfrac%7B-%5Cpi%20%5C%3A%7D%7B4%7D%2B%5Cfrac%7B-%5Cpi%20%5C%3A%5C%3A%7D%7B2%7D%5Cright%29%5Cright%5D)
( Simplify
for both
and
)
= ![\left(-\frac{3\pi }{4}\right)](https://tex.z-dn.net/?f=%5Cleft%28-%5Cfrac%7B3%5Cpi%20%7D%7B4%7D%5Cright%29)
( Substitute )
![-6\sqrt{2}\left(\cos \left(-\frac{3\pi }{4}\right)+i\sin \left(-\frac{3\pi }{4}\right)\right)](https://tex.z-dn.net/?f=-6%5Csqrt%7B2%7D%5Cleft%28%5Ccos%20%5Cleft%28-%5Cfrac%7B3%5Cpi%20%7D%7B4%7D%5Cright%29%2Bi%5Csin%20%5Cleft%28-%5Cfrac%7B3%5Cpi%20%7D%7B4%7D%5Cright%29%5Cright%29)
Now that we have this in trigonometric form, let's convert into standard form by applying the following identities ----- ( 2 )
sin(π / 4) = √2 / 2 = cos(π / 4)
( Substitute )
=
= ![-\frac{\left(-\sqrt{2}-\sqrt{2}i\right)\cdot \:6\sqrt{2}}{2}](https://tex.z-dn.net/?f=-%5Cfrac%7B%5Cleft%28-%5Csqrt%7B2%7D-%5Csqrt%7B2%7Di%5Cright%29%5Ccdot%20%5C%3A6%5Csqrt%7B2%7D%7D%7B2%7D)
=
= ![-3\sqrt{2}\left(-\sqrt{2}\right)-\left(-3\sqrt{2}\right)\sqrt{2}i](https://tex.z-dn.net/?f=-3%5Csqrt%7B2%7D%5Cleft%28-%5Csqrt%7B2%7D%5Cright%29-%5Cleft%28-3%5Csqrt%7B2%7D%5Cright%29%5Csqrt%7B2%7Di)
=
- Therefore our solution is option a.
Make a rectangular box that is 7/8 foot long, and 3/5 foot wide, then you just multiply the two together, I'm not gonna do it all for ya.
√96 simplified is 9.8
Use the Pythagorean theorem
Answer:
α + β = - ba and αβ = ca.
⇒ x2 + bax + ca = 0 (Since, a ≠ 0)
⇒ x2 - (α + β)x + αβ = 0, [Since, α + β = -ba and αβ = ca]
Step-by-step explanation:
pls mark brainlist
Answer:
I have seen racism play out in many ways in this world today. Here are some ways i've seen it in. MOSTLY, when a white person walks out of a store they can walk out just fine, but with black people, They have to check, and or scan them to make sure they arent stealing, and mostly if there was a black person involved or near and crime scene there always involved into the situation because the cops think they were in the crime. How so white people not so much.
*HOPE THIS HELPS !*
Step-by-step explanation: