What is the trigonometric form of # (-3+12i) #?

1 Answer
Jim G.
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)]#

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