Solve z=3-2i/(2+i)^2

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

Solve for z

$$z=\frac{1}{25}-\frac{18}{25}i=0.04-0.72i$$

Steps for Solving Linear Equation

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

$$z=\frac{3-2i}{3+4i}$$

Multiply both numerator and denominator of \frac{3-2i}{3+4i} by the complex conjugate of the denominator, 3-4i.

$$z=\frac{\left(3-2i\right)\left(3-4i\right)}{\left(3+4i\right)\left(3-4i\right)}$$

Do the multiplications in \frac{\left(3-2i\right)\left(3-4i\right)}{\left(3+4i\right)\left(3-4i\right)}.

$$z=\frac{1-18i}{25}$$

Divide 1-18i by 25 to get \frac{1}{25}-\frac{18}{25}i.

$$z=\frac{1}{25}-\frac{18}{25}i$$

Assign z

$$z≔\frac{1}{25}-\frac{18}{25}i$$