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

2 answers

tanΞΈ = 2/3, so
sinθ = 2/√13
cosθ = 3/√13
z = 5(cosΞΈ + i sinΞΈ)
Now just finish it off
The accepted answer for this is 15/sqrt13 + (10/sqrt13)i