Question B.2: Convert the following complex numbers into rectangular form:...

(a) Using Eq. (B.6),

z = x + jy = r \underline{/\theta} = r cosθ + jr sinθ            (B.6)

12 \underline{/-60^{\circ}} = 12 cos (−60°) + j12 sin (−60°) = 6 − j10.39

Note that θ = −60° is the same as θ = 360° − 60° = 300°.
(b) We can write

-50 \underline{/ 285^{\circ}} = −50 cos 285° − j50 sin 285° = −12.94 + j48.3

(c) Similarly,

8 e^{j 10^{\circ}} = 8 cos 10° + j8 sin 10° = 7.878 + j1.389

(d) Finally,

20 e^{-j \pi / 3} = 20 cos (−π/3) + j20 sin (−π/3) = 10 − j17.32