If #cos50^@+isin50^@#, a complex number in rectangular form, is written in polar form #r(costheta+isintheta)#, what is #r# and #theta# and how is it written in polar form?

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Answer 1 · 2018-01-04T15:09:14

#r=1# and #theta=50^@# and in polar form it is #1(cos50^@+isin50^@)#

A number #a+ib# in polar form is written as

#r(costheta+isintheta)#

Hence #a=rcostheta# and #b=rsintheta#

also squaring and adding them

#a^2+b^2=r^2cos^2theta+r^2sin^2theta#

= #r^2(cos^2theta+sin^2theta)=r^2xx1=r^2#

It is apparent in #cos50^@+isin50^@#, we have

#r^2=cos^2 50^@+sin^2 50^@=1# and hence #r=1#

and of course #theta=50^@#

and in polar form it is #1(cos50^@+isin50^@)#