Question

Given z1 = startroot 2 endroot (cosine (startfraction 3 pi over 4 endfraction) i sine (startfraction 3 pi over 4 endfraction) ) and z 2 = (cosine (startfraction pi over 2 endfraction) i sine (startfraction pi over 2 endfraction) ) , what is the value of z1 – z2?

Answer 1

The subtraction of complex numbers $z_{1} -z_{2}$ is cos(π)+i sin(π).

Given $z_{1} =\sqrt{2}$[cos(3π/4+i sin(3π/4) and $z_{2}$=cos (π/2) +i sin(π/2)

We have to find the value of $z_{1} -z_{2}$.

A complex number is a number that includes real number as well as a imaginary unit in which $i^{2} =1$. It looks like a+ bi.

We have to first solve $z_{1} and z_{2}$ and then we will be able to find the difference.

$z_{1} =$$\sqrt{2}$[ cos (3π/4)+i sin (3π/4)]

$=\sqrt{2}$[cos(π-π/4)+ i sin (π-π/4)]

=$\sqrt{2}$ [-cos(π/4)+sin (π/4)]

=$\sqrt{2}$(-1/$\sqrt{2}$+1/$\sqrt{2}$)

=$\sqrt{2} *0$

=0

$z_{2} =$cos(π/2)+i sin (π/2)

=0+i*1

=1

Now putting the values of $z_{1} and z_{2}$,

$z_{1} -z_{2} =0-1$

=-1

=-1+i*0

=cos (π)+i sin(π)

Hence the value of difference between $z_{1} and z_{2}$ is cos(π)+i sin(π).

Learn more about complex numbers at brainly.com/question/10662770

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