express complex number in polar form?

Question

(148/145 +51/145 i)

Answer 1

First, I'll rewrite in decimal form (to make it easier to read!):

z = 1.02069 + 0.351724i


Modulus is
SQRT(1.02069^2 + 0.351724^2) = 1.07959

Argument is
arctan(0.351724/1.02069) = 19.01 deg (or 0.331851 rad)

Answer 2

a = (1/145)(148 + 51 i)
a = (1/145) ( r /_ θ )

r ² = 148 ² + 51 ²
r = 156.5
θ = tan^(-1) ( 51 / 148 )
θ = 19°

a = (156 /145) (cos 19° + i sin 19°)
a = 1.08 (cos 19° + i sin 19° )
OR
a = 1.08 /_19°