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

Answer:

(a) 5.196+j3

(b) $6.403$  in polar form and $6.403e^{j51.34}$  in exponential form

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

$A_2=\sqrt{(4)^{2}+(5)^{2}}$

Also, in exponential form, A<b is written as $Ae^{jb}$

Therefore, $A_2=6.403$