Understanding Engineering Mathematics

Exercises on 12.8

1. Find ina+jbform and plot on Argand diagram:
   (i) The three values ofj^1 /^3
   (ii) The four values of( 1 +j)^1 /^4


2. Solve the following equations ina+jbform and plot the roots in the Argand plane.
   (i)x^6 − 1 = 0 (ii)x^3 + 8 = 0

Answer

1. (i)

√

3

2

+

1

2

j, −

√

3

2

+

1

2

j,−j

−j

y

x

1

√ 3

2

1

− + 2 j

√ 3

2

1

+ 2 j

0

(ii) 2^1 /^8

(

cos

(π

16

)

+jsin

(π

16

))

21 /^8

(

cos

(

9 π

16

)

+jsin

(

9 π

16

))

21 /^8

(

cos

(

17 π

16

)

+jsin

(

17 π

16

))

21 /^8

(

cos

(

25 π

16

)

+jsin

(

25 π

16

))

2 1/8

y

x

2 1/8 cos ( )^916 π + j 2 1/8 sin ( )^916 π

2 1/8 cos ( ) 16 π + j 2 1/8 sin ( ) 16 π

2 1/8 cos ( )^1716 π + j 2 1/8 sin ( )^1716 π

2 1/8 cos ( )^2516 π+ j 2 1/8 sin ( )^2516 π