Question

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)

Answer 1

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

Answer 2

`z_1=√(3)\left(cos\:(\pi )/(4)+i\:sin\:(\pi )/(4)\right)`

`z_2=√(6)\left(cos\:(3\pi \:)/(4)+i\:sin\:(3\pi \:)/(4)\right)`

`\cos \left((\pi )/(4)\right)=(√(2))/(2)`

`\sin \left((\pi )/(4)\right)=(√(2))/(2)`

`\cos \left((3\pi )/(4)\right)=-(√(2))/(2)`

`\sin \left((3\pi )/(4)\right)=(√(2))/(2)\\`

`Z_1*Z_2=√(3)\left(cos\:(\pi )/(4)+i\:sin\:(\pi )/(4)\right)\cdot √(6)\left(cos\:(3\pi \:)/(4)+i\:sin\:(3\pi \:)/(4)\right)`

`=√(3)\left((√(2))/(2)+\:i(√(2))/(2)\right)\cdot √(6)\left((-√(2))/(2)+\:i(√(2))/(2)\right)`

On simplifying, we get

`Z_1* Z_2 =-3√(2)`

Therefore, correct option is 1st option.