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

Operations of complex numbers in polar form quick check:

1. D

2. B

3. D

4. A



Answer 2

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 )