Solve 4z-3z=1-18i/2-i

$$4 z - 3 z = \frac { 1 - 18 i } { 2 - i }$$

Solve for z

$$z=4-7i$$

Steps for Solving Linear Equation

Combine 4z and -3z to get z.

$$z=\frac{1-18i}{2-i}$$

Multiply both numerator and denominator of \frac{1-18i}{2-i} by the complex conjugate of the denominator, 2+i.

$$z=\frac{\left(1-18i\right)\left(2+i\right)}{\left(2-i\right)\left(2+i\right)}$$

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$z=\frac{\left(1-18i\right)\left(2+i\right)}{2^{2}-i^{2}}$$

By definition, i^{2} is -1. Calculate the denominator.

$$z=\frac{\left(1-18i\right)\left(2+i\right)}{5}$$

Multiply complex numbers 1-18i and 2+i like you multiply binomials.

$$z=\frac{1\times 2+i-18i\times 2-18i^{2}}{5}$$

By definition, i^{2} is -1.

$$z=\frac{1\times 2+i-18i\times 2-18\left(-1\right)}{5}$$

Do the multiplications in 1\times 2+i-18i\times 2-18\left(-1\right).

$$z=\frac{2+i-36i+18}{5}$$

Combine the real and imaginary parts in 2+i-36i+18.

$$z=\frac{2+18+\left(1-36\right)i}{5}$$

Do the additions in 2+18+\left(1-36\right)i.

$$z=\frac{20-35i}{5}$$

Divide 20-35i by 5 to get 4-7i.

$$z=4-7i$$