Solve z=i^3-1+2i/2-i

$$z = i ^ { 3 } - \frac { 1 + 2 i } { 2 - i }$$

Solve for z

$$z=-2i$$

Steps for Solving Linear Equation

Calculate i to the power of 3 and get -i.

$$z=-i-\frac{1+2i}{2-i}$$

Multiply both numerator and denominator of \frac{1+2i}{2-i} by the complex conjugate of the denominator, 2+i.

$$z=-i-\frac{\left(1+2i\right)\left(2+i\right)}{\left(2-i\right)\left(2+i\right)}$$

Do the multiplications in \frac{\left(1+2i\right)\left(2+i\right)}{\left(2-i\right)\left(2+i\right)}.

$$z=-i-\frac{5i}{5}$$

Divide 5i by 5 to get i.

$$z=-i-i$$

Subtract i from -i to get -2i.

$$z=-2i$$

Assign z

$$z≔-2i$$