Solve (1-i)z=8+6i

$$( 1 - i ) z = 8 + 6 i$$

Solve for z

$$z=1+7i$$

Steps for Solving Linear Equation

Divide both sides by 1-i.

$$z=\frac{8+6i}{1-i}$$

Multiply both numerator and denominator of \frac{8+6i}{1-i} by the complex conjugate of the denominator, 1+i.

$$z=\frac{\left(8+6i\right)\left(1+i\right)}{\left(1-i\right)\left(1+i\right)}$$

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

$$z=\frac{\left(8+6i\right)\left(1+i\right)}{1^{2}-i^{2}}$$

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

$$z=\frac{\left(8+6i\right)\left(1+i\right)}{2}$$

Multiply complex numbers 8+6i and 1+i like you multiply binomials.

$$z=\frac{8\times 1+8i+6i\times 1+6i^{2}}{2}$$

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

$$z=\frac{8\times 1+8i+6i\times 1+6\left(-1\right)}{2}$$

Do the multiplications in 8\times 1+8i+6i\times 1+6\left(-1\right).

$$z=\frac{8+8i+6i-6}{2}$$

Combine the real and imaginary parts in 8+8i+6i-6.

$$z=\frac{8-6+\left(8+6\right)i}{2}$$

Do the additions in 8-6+\left(8+6\right)i.

$$z=\frac{2+14i}{2}$$

Divide 2+14i by 2 to get 1+7i.

$$z=1+7i$$