Respuesta :
The subtraction of complex numbers [tex]z_{1} -z_{2}[/tex] is cos(π)+i sin(π).
Given [tex]z_{1} =\sqrt{2}[/tex][cos(3π/4+i sin(3π/4) and [tex]z_{2}[/tex]=cos (π/2) +i sin(π/2)
We have to find the value of [tex]z_{1} -z_{2}[/tex].
A complex number is a number that includes real number as well as a imaginary unit in which [tex]i^{2} =1[/tex]. It looks like a+ bi.
We have to first solve [tex]z_{1} and z_{2}[/tex] and then we will be able to find the difference.
[tex]z_{1} =[/tex][tex]\sqrt{2}[/tex][ cos (3π/4)+i sin (3π/4)]
[tex]=\sqrt{2}[/tex][cos(π-π/4)+ i sin (π-π/4)]
=[tex]\sqrt{2}[/tex] [-cos(π/4)+sin (π/4)]
=[tex]\sqrt{2}[/tex](-1/[tex]\sqrt{2}[/tex]+1/[tex]\sqrt{2}[/tex])
=[tex]\sqrt{2} *0[/tex]
=0
[tex]z_{2} =[/tex]cos(π/2)+i sin (π/2)
=0+i*1
=1
Now putting the values of [tex]z_{1} and z_{2}[/tex],
[tex]z_{1} -z_{2} =0-1[/tex]
=-1
=-1+i*0
=cos (π)+i sin(π)
Hence the value of difference between [tex]z_{1} and z_{2}[/tex] is cos(π)+i sin(π).
Learn more about complex numbers at https://brainly.com/question/10662770
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