Asked by anonymous
Find the square roots of z=5−12i
Answers
Answered by
Reiny
z = 5 - 12i
|z| = √(25 + 144) = √169 = 13
tanθ = -12/5
θ = 292.62°
then 5-12i = 13cis 292.62°
(5-12i)^(1/2) = √13cis146.309..°
= √13cos146.309.. + √13sin146.309..
= -3 + 2i <---- primary root
second root = √13cos(146.309..+180) + √13sin(146.309..+180)
= 3 - 2i
|z| = √(25 + 144) = √169 = 13
tanθ = -12/5
θ = 292.62°
then 5-12i = 13cis 292.62°
(5-12i)^(1/2) = √13cis146.309..°
= √13cos146.309.. + √13sin146.309..
= -3 + 2i <---- primary root
second root = √13cos(146.309..+180) + √13sin(146.309..+180)
= 3 - 2i