Question

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

Answer 1

`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))`