HOW DO I WRITE THE POLAR FORM OF isqrt2 sqrt6 iSolutionisqr

HOW DO I WRITE THE POLAR FORM OF i(sqrt2 - sqrt6 i)?

Solution

i(sqrt 2 - sqrt 6 i)

distributing i

i sqrt 2 - sqrt6 i²

i sqrt2 + sqrt6

sqrt 6 + isqrt 2

R= sqrt(x²+y²) = sqrt( (sqrt6)²+(sqrt2)²) =sqrt 8=2sqrt2

theta= tan^-1(y/x) = tan^-1(sqrt2/sqrt6)=pi/6

hence the required polar form is

2sqrt2 (cos pi/6 +i sin pi/6)