What is the trigonometric form of # (2-i)*(1+i) #?

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Answer 1 · 2017-09-15T13:21:19

See explanation.

First we have to multiply the numbers:

#(2-i)*(1+i)=2+2i-i-i^2=2+i+1=3+i#

Now we have to write the result #3+i# in trigonometric form:

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

Now we have to find the angle using:

#cosvarphi=(re(z))/|z|#

#cosvarphi=3/sqrt(10)=(3sqrt(10))/10~~0.949#

From this we have #varphi ~~18.43^o#.

Finally we can write the result as:

#z=sqrt(10)*(cos18.43^o + isin18.43^o)#