How do you multiply (-3-i)(4+2i) (−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 (−3−i)(4+2i)=−12−6i−4i−2i2 [
i^2 = -1 ] i2=−1] hence
- 12 -10i + 2 = -10 - 10i color(black)(" is the result ") −12−10i+2=−10−10i is the result To convert to trig form require to find modulus r , and
argument,theta θ r =
sqrt( (-10)^2 + (-10)^2 ) = sqrt200 =10sqrt2√(−10)2+(−10)2=√200=10√2 and
theta = tan^-1 ((-10)/-10) = tan^-1 (1 )= pi/4 θ=tan−1(−10−10)=tan−1(1)=π4 in trig form :
10sqrt2 (cos(pi/4) + isin(pi/4))10√2(cos(π4)+isin(π4))
