Question

HELP FAST PLEASE

Given z1=2(cos pi/6+i sin pi/6) and z2=3(cos pi/4+i sin pi/4), find z1z2 where 0 is equal to or less than theta and theta is less tan 2pi

Answer 1

By using Euler’s formula which state that:

            e∧(iΘ)  = cos Θ + i sin Θ

So,     z₁ = 2 ( cos π/6  + i  sin π/6 ) = 2 e∧(i π/6)
And    z₂ = 3 ( cos π/4  + i  sin π/4 ) = 3 e∧(i π/4)

Then z₁ * z₂ = 2 e∧(i π/6) * 3 e∧(i π/4) = 6 e∧[i (π/6 + π/4)]
                    = 6 e∧(i 5π/12)
                    = 6 ( cos 5π/12  + i  sin 5π/12 )