Question

Given the complex numbers: A1 = 6∠30° and A2 = 4 + j5 a. Convert A1 to rectangular form.b. Convert A2 to polar and exponential form.

Answer 1

(a) 5.196+j3

(b)
`6.403<51.34^(\circ)` in polar form and
`6.403e^(j51.34)` in exponential form

Step-by-step explanation:

To convert the polar number into rectangular form

`A_1= 6(cos 30^(\circ)+ j sin 30^(\circ))\\= 6 cos 30^(\circ)+ j6 sin30^(\circ)\\ =(6)(0.866)+j(6)(0.5)\\= 5.196+ j3`

Therefore, the rectangular form is 5.196+j3

To convert the complex number into polar form

`A_2=\sqrt{(4)^(2)+(5)^(2)}<tan^(-1)(\frac {5}{4})\\= √(16+25)<tan^(-1)(1.25)\\=√(41)<51.34^(\circ)\\= 6.403<51.34^(\circ)`

Also, in exponential form, A<b is written as
`Ae^(jb)`

Therefore,
`A_2=6.403<51.34^(\circ)=6.403e^(j51.34)`