Solve (3+4i)z=5i^2016

$$( 3 + 4 i ) z = 5 i ^ { 2016 }$$

Solve for z

$$z=\frac{3}{5}-\frac{4}{5}i=0.6-0.8i$$

Steps for Solving Linear Equation

Calculate i to the power of 2016 and get 1.

$$\left(3+4i\right)z=5\times 1$$

Multiply 5 and 1 to get 5.

$$\left(3+4i\right)z=5$$

Divide both sides by 3+4i.

$$z=\frac{5}{3+4i}$$

Multiply both numerator and denominator of \frac{5}{3+4i} by the complex conjugate of the denominator, 3-4i.

$$z=\frac{5\left(3-4i\right)}{\left(3+4i\right)\left(3-4i\right)}$$

Do the multiplications in \frac{5\left(3-4i\right)}{\left(3+4i\right)\left(3-4i\right)}.

$$z=\frac{15-20i}{25}$$

Divide 15-20i by 25 to get \frac{3}{5}-\frac{4}{5}i.

$$z=\frac{3}{5}-\frac{4}{5}i$$