How do you add #(-1+3i)+(7-3i)# in trigonometric form?

1 Answer
Feb 26, 2016

Adding in rectangular form then converting to trigonometric form gives
#color(white)("XXX")6(cos(0)+isin(0))#

Explanation:

Confession: I don't know any easy way to do the addition in trigonometric form (multiplication and division is relatively easy).

However we can add:
#color(white)("XXX")(-1+3i)+(7-3i)#
#color(white)("XXXXXX")=(-1+7)+(3i-3i)#
#color(white)("XXXXXX")=6+0i#

which translates easily into trigonometric form #r(cos(theta)+isin(theta))#
with #r=sqrt(6^2+0^2) = 6#
and #theta = arctan(0/6)= arctan(0) = 0#