Compute the rectangular coordinates for point A to 2 decimal places given the po

Question

Compute the rectangular coordinates for point A to 2 decimal places given the polar coordinates. Given: (r, theta) = (20.12,243.44 degree) Find: The corresponding rectangular coordinates for the point. Solution: Express both coordinates to 2 decimal places. (x,y) = (,) Given the complex number A = - 3+ - 4i Calculate the magnitude of A (rounded to 3 decimal places). Calculate the phase angle of A(rounded to 2 decimal places). ComplexNumbers Rectangular to Polar Given: Compute the magnitude |z| and the Phase/Angle Phi for the complex number 1 + 0i Answer: Please enter your answer using 2 decimal places only Magnitude = Phase/Angle =

Explanation / Answer

(x, y) = ( r cos theta , r sin theta )

(x,y) = ( 20.12*cos 243.44 , 20.12*sin 243.44)

(x,y) = (-9.00 , -18.00)

2.
A = -3 - 4i

magnitude = sqrt ( 3^2 + 4^2) = sqrt (25)= 5

phase angle = pi + arc tan ( 4/3) = 233.13 degrees

3. z = 1+ 0 i

magnitude =sqrt (1^2+ 0)= 1
phase angle = arc tan ( 0/1) = 0 degrees/radians

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