What is the trigonometric form of # (-5+12i) #?

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Answer 1 · 2016-01-04T20:57:42

13 ( cos1.96 +isin1.96)

the complex number z = x + iy can be written in trigonemetric form as # z = r( costheta + isintheta)#

the modulus r =# sqrt(x^2 + y^2)#

and the argument # theta # is found by using

# tantheta = y/x #

in this case # r = sqrt ((-5)^2 +(12)^2)#

# = sqrt (25 + 144 ) = sqrt169 = 13 #

# tanalpha = y/x = 12/5 =2.4 # and so

# alpha = 1. 176 #

arg z = # ( pi - 1.176 )# = 1.96

In this case z is in the 2nd quadrant and so the required argument is #( pi - alpha) #