Answer:
The answer is B!
Step-by-step explanation:
EDG 2021, have a great day!!
The sum of given complex numbers in polar form as [tex]w+z=cos(\frac{\pi}{2} )+i~sin(\frac{\pi}{2} )[/tex]
"The number of the type a + ib is called as complex number, where a, b are real numbers and [tex]i=\sqrt{-1}[/tex] "
"The polar form of a complex number z = x + iy is [tex]z=r(cos\theta+i~sin\theta)[/tex] where [tex]r=\sqrt{x^2+y^2}[/tex] and [tex]\theta=tan^{-1}({\frac{y}{x} })[/tex] "
For given question,
We have been given two complex numbers in polar form.
[tex]w=4(cos(\frac{\pi}{2} )+i~sin(\frac{\pi}{2} ))~,z=3(cos(\frac{3\pi}{2} )+i~sin(\frac{3\pi}{2} ))[/tex]
The sum of given complex numbers would be,
[tex]w+z= 4(cos(\frac{\pi}{2} )+i~sin(\frac{\pi}{2} ))+3(cos(\frac{3\pi}{2} )+i~sin(\frac{3\pi}{2} ))[/tex]
We know that
[tex]cos(\frac{\pi}{2} )=0\\\\sin(\frac{\pi}{2} )=1\\\\cos(\frac{3\pi}{2} )=0\\\\sin(\frac{\pi}{2} )=-1[/tex]
So, the sum of given complex numbers would be,
[tex]w+z\\\\= 4(cos(\frac{\pi}{2} )+i~sin(\frac{\pi}{2} ))+3(cos(\frac{3\pi}{2} )+i~sin(\frac{3\pi}{2} ))\\\\=4(0+i(1))+3(0+i(-1))\\\\=4(i)+3(-i)\\\\=i\\\\=0+i[/tex]
We can write above sum of complex numbers in polar form as,
[tex]0+i=cos(\frac{\pi}{2} )+i~sin(\frac{\pi}{2} )[/tex]
Therefore, the sum of given complex numbers in polar form as [tex]w+z=cos(\frac{\pi}{2} )+i~sin(\frac{\pi}{2} )[/tex]
Learn more about complex numbers here:
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