Answer to Question #187973 in Complex Analysis for Muzala Seleji

Question #187973

Solvetheequationsbelowandhence,showthesolutionsoftheseequationsontheArganddiagram:(i)z4−i=0(ii)z3=−√3−i(iii)z5=−18i(iv)z=16i1+i18(v)z=1+i√3+i16


1
Expert's answer
2021-05-07T10:09:43-0400

(i)"z4-i=0"

"4(x+iy)-i=0\\Rightarrow 4x+(4y-1)i=0\\Rightarrow x=0 \\text{ and }y=\\dfrac{1}{4}"


(ii) "z3=-\\sqrt{3}-i"

"3(x+iy)+\\sqrt{3}+i=0\\Rightarrow (3x+\\sqrt{3})+i(y+1)=0\\Rightarrow x=\\dfrac{-1}{\\sqrt{3}}, y=-1"


(iii)"z5=-18i"

"5(x+iy)+18i=0\\Rightarrow 5x+i(y+18)=0\\Rightarrow x=0,y=-18"


(iv) "z=16i+18i"

"x+iy=34i\\Rightarrow x=0,y=34"


(v) "z=1+i\\sqrt{3}+16i"

"x+iy=1+i(\\sqrt{3}+16)\\Rightarrow x=1,y=\\sqrt{3}+16"


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