Question

Given two complex numbers z and w such that z=(1+i)w+(3-i)w^_ where w^_is the conjugate of w which of the following is w^_ in terms of z and z^_

Answer 1

$\displaystyle z = (1+i)w+(3-i)\overline{w}\\ \text{Making $\overline{w}$ the subject of the formula, we have}\\ \overline{w} = \frac{z-(1+i)w}{3-i}\\ \text{Next we rationalize the fraction by multiplying the numerator and denominator by }\\ \text{3+i to obtain }\\ \frac{z(3+i)-(2+4i)}{10}$