How do you divide i+27i+3 in trigonometric form?

1 Answer
Jan 5, 2018

29058(cos(40.24)isin(40.24))

Explanation:

For a complex number z=a+bi, we can rewrite it in the form z=r(cosθ+isinθ), where r=a2+b2 and θ=tan1(ba)

z1=2+i
r1=22+12=5
θ1=tan1(12)
z1=5(cos(tan1(12))+isin(tan1(12))

z2=3+7i
r2=32+72=58
θ2=tan1(73)
z2=5(cos(tan1(73))+isin(tan1(73))

z1z2=r1r2(cos(θ1θ2)+isin(θ1θ2))

z1z2=558(cos(tan1(12)tan1(73))+isin(tan1(12)tan1(73)))
29058(cos(40.24)+isin(40.24))

Since cos(x)=cos(x) and sin(x)=sin(x)

=29058(cos(40.24)isin(40.24))