Solve z=1+7i/(2-i)^2

$$z = \frac { 1 + 7 i } { ( 2 - i ) ^ { 2 } }$$

Solve for z

$$z=-1+i$$

Steps for Solving Linear Equation

Calculate 2-i to the power of 2 and get 3-4i.

$$z=\frac{1+7i}{3-4i}$$

Multiply both numerator and denominator of \frac{1+7i}{3-4i} by the complex conjugate of the denominator, 3+4i.

$$z=\frac{\left(1+7i\right)\left(3+4i\right)}{\left(3-4i\right)\left(3+4i\right)}$$

Do the multiplications in \frac{\left(1+7i\right)\left(3+4i\right)}{\left(3-4i\right)\left(3+4i\right)}.

$$z=\frac{-25+25i}{25}$$

Divide -25+25i by 25 to get -1+i.

$$z=-1+i$$

Assign z

$$z≔-1+i$$