Write on the trigonometric form the following complex number: -3(Cos#pi#/4 + isin#pi#/4) ?

Question

1756 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-02-02T21:31:37

see explanation.

Well, I think of #-3(cos(pi/4)+isin(pi/4))#, or #-3cis(pi/4)#, as trig form. An alternative uses Euler's formula,

#r*e^(itheta) = 4(cos(theta)+isin(theta))#,

so we can also write it as #-3e^(pi/4i)#.

We could also write it in rectangular, or standard, form:

Since #cos(pi/4) =sin(pi/4) = sqrt(2)/2# we have:

#-3(cos(pi/4)+isin(pi/4)) = -3(sqrt(2)/2 + sqrt(2)/2i)#

#=-(3sqrt(2))/2 -(3sqrt(2))/2i#