Question

There is an angle 𝜃 in quadrant I such that tan 𝜃 = 2/3. Convert the complex number z = 5 cis 𝜃 from polar to rectangular form.

Answer 1

tanθ = 2/3, so
sinθ = 2/√13
cosθ = 3/√13
z = 5(cosθ + i sinθ)
Now just finish it off

Answer 2

The accepted answer for this is 15/sqrt13 + (10/sqrt13)i