Find all the square roots of the complex number 14i. Write the square roots in polar (re^i) form,
with the smaller angle first. Give angles in degress
Solution
this is the polar form r(cos()+isin())
we compare it with 1-4i
rcos =1
rsin=-4
squaring and adding them
r^2(cos^2 +sin^2) = 1 +(-4)^2
r^2 = 1+16
r= sqrt(17) =4.1
tan = -4/1
= arc tan(-4)
= -76 degree
square root of r(cos()+isin()) is ±r(cos(/2)+isin(/2)).
square root form is ±(4.1) (cos(-76/2) + isin(-76/2)
±4.1(cos38 -isin38)
in polar form 4.1 e^(-38i).
Find all the square roots of the complex number 14i. Write the squar.pdf
1. Find all the square roots of the complex number 14i. Write the square roots in polar (re^i) form,
with the smaller angle first. Give angles in degress
Solution
this is the polar form r(cos()+isin())
we compare it with 1-4i
rcos =1
rsin=-4
squaring and adding them
r^2(cos^2 +sin^2) = 1 +(-4)^2
r^2 = 1+16
r= sqrt(17) =4.1
tan = -4/1
= arc tan(-4)
= -76 degree
square root of r(cos()+isin()) is ±r(cos(/2)+isin(/2)).
square root form is ±(4.1) (cos(-76/2) + isin(-76/2)
±4.1(cos38 -isin38)
in polar form 4.1 e^(-38i)
