Solve for z
z=1-i
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z=\frac{1+i}{i}
Divide both sides by i.
z=\frac{\left(1+i\right)i}{1i^{2}}
Multiply both numerator and denominator of \frac{1+i}{i} by imaginary unit i.
z=\frac{\left(1+i\right)i}{-1}
By definition, i^{2} is -1. Calculate the denominator.
z=\frac{i+i^{2}}{-1}
Multiply 1+i times i.
z=\frac{i-1}{-1}
By definition, i^{2} is -1.
z=\frac{-1+i}{-1}
Reorder the terms.
z=1-i
Divide -1+i by -1 to get 1-i.
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