How do you multiply # (-3-i)(4+2i) # in trigonometric form?
1 Answer
Jan 22, 2016
Explanation:
Multiply out brackets (distributive law ) -using FOIL method.
# (-3 - i )(4 + 2i ) = - 12 -6i - 4i -2i^2 # [
# i^2 = -1 ] # hence
# - 12 -10i + 2 = -10 - 10i color(black)(" is the result ") # To convert to trig form require to find modulus r , and
argument,#theta # r =
# sqrt( (-10)^2 + (-10)^2 ) = sqrt200 =10sqrt2# and
#theta = tan^-1 ((-10)/-10) = tan^-1 (1 )= pi/4 # in trig form :
# 10sqrt2 (cos(pi/4) + isin(pi/4))#
