What is the trigonometric form of #-1+3i#?

Question

1418 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-02-20T10:59:28

The trignometric form is #z=sqrt(10)(cos(108.4^@)+isin(108.4^@))#, #[mod 360^@]#

The complex number is

#z=-1+3i#

The polar form of #z=a+ib#

is

#z=r(costheta+isintheta)#

Where,

#r=|z|#

#costheta=a/|z|#

#sintheta=b/|z|#

Here,

#|z|=r=sqrt((-1)^2+(3)^2)=sqrt(10)#

#costheta=-1/sqrt(10)#

#sintheta=3/sqrt(10)#

#theta=108.4^@#

Therefore,

#z=sqrt(10)(cos(108.4^@)+isin(108.4^@))#, #[mod 360^@]#