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Help!! Which of the following best represents Z1 • Z2 select all that apply

(Tell me using 1st, 2nd, 3rd, 4th, 5th , 6th don’t write the whole options)

Help Which of the following best represents Z1 Z2 select all that apply Tell me using 1st 2nd 3rd 4th 5th 6th dont write the whole options class=

Respuesta :

[tex]z_1=\sqrt{3}\left(cos\:\frac{\pi }{4}+i\:sin\:\frac{\pi }{4}\right)[/tex]

[tex]z_2=\sqrt{6}\left(cos\:\frac{3\pi \:}{4}+i\:sin\:\frac{3\pi \:}{4}\right)[/tex]

[tex]\cos \left(\frac{\pi }{4}\right)=\frac{\sqrt{2}}{2}[/tex]

[tex]\sin \left(\frac{\pi }{4}\right)=\frac{\sqrt{2}}{2}[/tex]

[tex]\cos \left(\frac{3\pi }{4}\right)=-\frac{\sqrt{2}}{2}[/tex]

[tex]\sin \left(\frac{3\pi }{4}\right)=\frac{\sqrt{2}}{2}\\[/tex]

[tex]Z_1*Z_2=\sqrt{3}\left(cos\:\frac{\pi }{4}+i\:sin\:\frac{\pi }{4}\right)\cdot \sqrt{6}\left(cos\:\frac{3\pi \:}{4}+i\:sin\:\frac{3\pi \:}{4}\right)[/tex]

[tex]=\sqrt{3}\left(\frac{\sqrt{2}}{2}+\:i\frac{\sqrt{2}}{2}\right)\cdot \sqrt{6}\left(\frac{-\sqrt{2}}{2}+\:i\frac{\sqrt{2}}{2}\right)[/tex]

On simplifying, we get

[tex]Z_1* Z_2 =-3\sqrt{2}[/tex]

Therefore, correct option is  1st option.

Answer:

Hi I just took this lesson and got it right. Hope this helps!

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