Answer:
(a) 5.196+j3
(b) [tex]6.403<51.34^{\circ}[/tex] in polar form and [tex]6.403e^{j51.34}[/tex] in exponential form
Explanation:
To convert the polar number into rectangular form
[tex]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[/tex]
Therefore, the rectangular form is 5.196+j3
To convert the complex number into polar form
[tex]A_2=\sqrt{(4)^{2}+(5)^{2}}<tan^{-1}(\frac {5}{4})\\= \sqrt{16+25}<tan^{-1}(1.25)\\=\sqrt{41}<51.34^{\circ}\\= 6.403<51.34^{\circ}[/tex]
Also, in exponential form, A<b is written as [tex]Ae^{jb}[/tex]
Therefore, [tex]A_2=6.403<51.34^{\circ}=6.403e^{j51.34}[/tex]
