Understanding Engineering Mathematics

Answers

− 3 + 2 j

j

1

0

2 +j

1 −j

− 3 j

− 3 − 2 j

y

x

(i) 1^ ( 0 ) (ii) 1^

(π

2

)

(iii) 3^

(

−

π

2

)

(iv)

√

2

(

−

π

4

)

(v)

√

5

(

Tan−^1

(

1

2

))

(vi)

√

13

(

π+Tan−^1

(

2

3

))

(vii)

√

13

(

π−Tan−^1

(

2

3

))

(Tan−^1 denotes the principal value)

2. (i) 2 (ii) − 3 (iii) j (iv) −

3

√

2

+

3

√

2

j

(v)

1

2

−

√

3

2

j (vi) − 2 j

12.4 Multiplication in polar form

Now comes the pay-off of polar forms – multiplication of complex numbers in such form is
simplicity itself – indeed it reduces tomultiplication ofmodulii andaddition ofargument.
See for yourself:

Problem 12.7

Multiply .q 1 /and .q 2 /, use the compound angle formulae (187

➤

)and

hence show that

r 1 .q 1 /r 2 .q 2 /=r 1 r 2  .q 1 Yq 2 /