Question

Find A and B1 -1 1+j 21 l1-A^ eB, with 0A, and -180 B, 180 Solve without a calculator Given Variables: a :2 b:2 Determine the following: A1 () B1 (degrees)

Answer 1

To find A_1 & B_1 v_1 = b squareroot 2 J I_1 = v_1/z_1 & z_1 = (aI + a/1 + I)^-1 I_1 = A_1 middot e^j B_1: A_1 greaterthanorequalto 0, Vertical-bar B Vertical-bar < 180 degree i.e -180 degree < B < 180 a = b = 2 Lets do simplication for z_1 z_1 = (aJ + a/1 + J)^-1 = (2J + 2/1 + J)^-1 1/z_1 = ((1 + J) 2J + 2/1 + J) = (2J + 2J^2 + 2/1 + J) 1/z_1 = (2J - 2 + 2)/1 + J = 2J/(1 + J) (Because J^2 = -I) 1/z_1 = 2J(1 - J)/(1 + J) (1 - J) = 2J - 2J^2/(1 + 1) (Because Rationalising) 1/z_1 = 2J + 2/2 = (1 + J) 1/z_1 = (1 + J) (1) Now I_1 = v_1/z_1 = v_1 times 1/z_1 = b squareroot 2 J middot (1 + J) (Therefore from (1) 1/z_1 = 1 + J)

Hope it helps you out.

Incase any doubt please feel free to ask.

I will be happy to help you.

Put your thumbs up,if you like it!

Thanks!!

Note : value of angle B is -45° which may also be written as 180°-45= 135°. Choose whichever you prefer. However as B = tan-1(1/-1) = 135° is best value. As point (a+jb= -1+J1) lies in 2nd quadrant.