Тригонометрическая форма имеет вид a+bi=r(cosφ+isinφ), где r=√(a²+b²);
φ=arctg(b/a)
1)a=6cos(π/10) b=-6sin(π/10) r=6√(cos²(π/10)+sin²(π/10))=6
φ=arctg(-6sin(π/10) /6cos(π/10)) =arctg(-tg(π/10))=
arctg(tg(π-π/10))=arctg(tg(9π/10)=9π/10
6cos(π/10)-i-6sin(π/10)=6(cos(9π/10)+isin(9π/10))
2)a=2sin63⁰ b=2cos63⁰ r=2√(sin²63⁰+cos²63⁰)=2
φ=arctg(2cos63⁰/2sin63⁰)=arctg(ctg63⁰)=arctg(ctg(90⁰-37⁰))=arctg(tg37⁰)=37⁰
2sin63⁰ +i2cos63⁰ =2(cos37⁰+isin37⁰)
3)a=-4√3 b=12 r=√(16*3+144)=√192=√(64*3)=8√3
φ=arctg(-12/(4√3))=arctg(-√3)=π-arctg√3=π-π/3=2π/3
-4√3+i12=8√3(cos(2π/3)+isin(2π/3))