How do you multiply # (-3-i)(4+2i) # in trigonometric form?

1 Answer
Jan 22, 2016

# 10sqrt2 (cos(pi/4) + isin(pi/4)) #

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))#