Expert: Steve Holleran - 5/27/2008

Question
Convert the following to trigonometric form:
1) -5-i
2) (4 sqrt5) - 4i
3) -9-(2sqrt10i)

thank you!

Answer
Hi Cruz,  

1.  Okay, for z = -5 - i, we have the modulus is sqrt(5^2 + 1^2) = rt(26) , and the angle is arctan(-1/-5) = .197 radians.  Since the number is in the 3rd quadrant, add pi to the reference angle and you have

               z = rt(26) * (cos 3.339 + i * sin 3.339)

                 = 5.099 cis 3.339

2. This one has modulus sqrt(4rt(5)^2 + 4^2) = rt(96) = 9.79
and the angle is arctan(-4/4rt(5)) = -0.42 radians, so

               z = 9.79 cis (-0.42)

3.  The modulus her is sqrt(9^2 + 2rt(10)^2 ) = 11
and the angle is arctan(-2rt(10)/-9) = 0.612, but again you have to add pi since the number is in the 3rd quadrant, so

               z = 11 cis 3.754

Hope this helps.
Steve