arg (z-iz+i)=π3

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