How do you divide #( -i+1) / (2i -7 )# in trigonometric form?

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Answer 1 · 2018-06-24T06:03:03

#color(magenta)(=> 0.1943 ( -0.8742 - i 0.4856)#

#z_1 / z_2 = (r_1 / r_2) (cos (theta_1 - theta_2) + i sin (theta_1 - theta_2))#

#z_1 = 1 - i, z_2 = -7 + i 2#

#r_1 = sqrt(1^2 + 1^2) = sqrt 2#

#theta_1 = tan ^ (-1) (-1/1) = tan *-1 (-1) = -45 ^@ = 315^@, " IV Quadrant"#

#r_2 = sqrt((-7)^2 + (2)^2) = sqrt 53#

#theta_2 = tan ^-1 (2/ -7) = -15.95^@ = 164.05^@, " II Quadrant"#

#z_1 / z_2 = sqrt(2/53) (cos (315- 164.05) - i sin (315 - 164.05))#

#color(magenta)(=> 0.1943 (- 0.8742 - i 0.4856)#