i(sqrt 6 - sqrt 2 i)

Question

find the polar form with the argument Θ between o and 2pi

Answer 1

In rectangular form z = a + ib:

 

     z = i(sqrt 6 - sqrt 2 i) = √2 + i√6

 

In polar form z = r∠θ.  First find r:

 

     r = √(√2)² + (√6)²) = √8 = 2√2

 

Now find θ:

 

     θ = arctan(√6/√2) = arctan(√3) = 60°

 

Final polar form:

 

     z = 2√2 ∠60°

You can use pi/3 in place of 60 degrees if you prefer radians.