Solve for z arg ((z-i)/(z+i))=pi/3

arg (z-iz+i)=π3
Set up the rational expression with the same denominator over the entire equation.
Multiply each term by a factor of 1 that will equate all the denominators. In this case, all terms need a denominator of 3(z+i). The z-iz+i expression needs to be multiplied by 33 to make the denominator 3(z+i). The π3 expression needs to be multiplied by z+iz+i to make the denominator 3(z+i).
z-iz+i⋅33=π3⋅z+iz+i
Multiply the expression by a factor of 1 to create the least common denominator (LCD) of 3(z+i).
(z-i)(3)
Simplify.
Apply the distributive property.
z⋅3-i⋅33(z+i)=π3⋅z+iz+i
Simplify the expression.
Move 3 to the left of z.
3⋅z-i⋅33(z+i)=π3⋅z+iz+i
Multiply 3 by -1.
3z-3i3(z+i)=π3⋅z+iz+i
3z-3i3(z+i)=π3⋅z+iz+i
3z-3i3(z+i)=π3⋅z+iz+i
Multiply the expression by a factor of 1 to create the least common denominator (LCD) of 3(z+i).
π(z+i)
Apply the distributive property.
3z-3i3(z+i)=πz+πi3(z+i)
3z-3i3(z+i)=πz+πi3(z+i)
Since the expression on each side of the equation has the same denominator, the numerators must be equal.
3z-3i=πz+πi
Subtract πz from both sides of the equation.
3z-3i-πz=πi
Move πi to the left side of the equation by subtracting it from both sides.
3z-3i-πz-πi=0
Solve for z arg ((z-i)/(z+i))=pi/3

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