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:

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

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