How do you add #(2-8i)+(-2+4i)# in trigonometric form?

1 Answer
Alan P.
Dec 23, 2015

#(2-8i)+(-2+4i)= 4(cos((3pi)/2)+isin((3pi)/2))#

Explanation:

I will assume that we are allowed to do the addition in rectangular form and then convert the answer into trigonometric form.

#{: (,,"(",2,-8i,")"), ("+",,"(",-2,+4i,")"), (,,,"-------","-------",), ("=",,"(",0,-4i,")") :}#

The general trigonometric form is
#color(white)("XXX")abs(z)(cos(theta)+isin(theta))#
where
#color(white)("XXX")abs(z)# is the distance from the origin (in the complex plane)
and
#color(white)("XXX")#theta# is the angle of the point (relative to the positive Real axis in the complex plane)
enter image source here

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