#z_1 * z_2 = (r_1 * r_2) * ((cos theta_1 + theta_2) + i sin (theta_1 + theta_2))#
#z_1 = (1 + 2 i), z_2 = (2 - 5 i)#
#r_1 = sqrt (1^2 + 2^2) = sqrt (5)#
#theta _1 = tan ^-1 (2/1) = 63.43^@, " I quadrant"#
#r_2 = sqrt (2^2 = -5^2) = sqrt (29)#
#theta _2 = tan ^-1 (-5/2) = 291.8^@ , " IV quadrant"#
#z_1 * z_2 = (sqrt 5 * sqrt 29) * (cos(63.43 + 291.8) + i (63.43 + 291.8))#
#color(orange)((1 + 2 i)* (2 - 5 i) = 12.04 * (0.9965 -+ i 0.0832)#