Convert the following complex numbers into rectangular form:

(a) 12∠− 60°, (b) −50∠285°, (c) $8 e^{j 10^{\circ}}$ , (d) $20 e^{-j \pi / 3}$ .

Question

Convert the following complex numbers into rectangular form:

(a) 12∠− 60°, (b) −50∠285°, (c) [latex] 8 e^{j 10^{\circ}} [/latex] , (d) [latex] 20 e^{-j \pi / 3} [/latex].

Accepted Answer

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

[latex] z=x+j y=r \angle heta=r \cos heta+j r \sin heta [/latex] (B.6)

[latex] 12 \angle-60^{\circ}=12 \cos \left(-60^{\circ} ight)+j 12 \sin \left(-60^{\circ} ight)=6-j 10.39 [/latex]

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

[latex] -50 \angle 285^{\circ}=-50 \cos 285^{\circ}-j 50 \sin 285^{\circ}=-12.94+j 48.3 [/latex]

(c) Similarly,

[latex] 8 e^{j 10^{\circ}}=8 \cos 10^{\circ}+j 8 \sin 10^{\circ}=7.878+j 1.389 [/latex]

(d) Finally,

[latex] 20 e^{-j \pi / 3}=20 \cos (-\pi / 3)+j 20 \sin (-\pi / 3)=10-j 17.32 [/latex]

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