What is the trigonometric form of # (-3+12i) #?
1 Answer
Feb 4, 2016
# sqrt153[cos(1.81) + isin(1.81)]#
Explanation:
To convert to trig. form , require r , the modulus and
# theta, #
the argument.
#• r =sqrt(x^2 + y^2)#
#• theta = tan^-1 (y/x) # Here x = -3 and y = 12
# rArr r = sqrt((-3)^2 + 12^2) = sqrt(9+144) = sqrt153 # [ -3 + 12i is a point in the 2nd quadrant and care must be taken to ensure that
#theta color(black)(" is in this quadrant")# ]
# theta = tan^-1(12/-3) = tan^-1(-4) = -1.33color(black)(" radians")# and so
#theta = (pi-1.33) = 1.81color(black)(" radians")#
#rArr (-3+12i) = sqrt153[cos(1.81) + isin(1.81)]#
