What is the trigonometric form of (5-2i)(2+3i) ?

1 Answer
Jan 6, 2016

sqrt(377){cos(tan^-1(11/16))+isin(tan^-1(11/16))}

Explanation:

(5-2i)(2+3i)

Multiply using FOIL

(5)(2)+5(3i)+(-2i)(2)+(-2i)(3i)
10+15i-4i-6i^2
=10+11i-6(-1) since i^2=-1
=10+6+11i
=16+11i

Trigonometric form is r(cos(theta)+isin(theta))
if z=x+iy

r=sqrt(x^2+y^2) and theta = tan^-1(y/x)

r=sqrt(16^2+11^2) and theta = tan^-1(11/16)
r=sqrt(256+121)
r=sqrt(377)
Trigonometric form

sqrt(377){cos(tan^-1(11/16))+isin(tan^-1(11/16))}