Solve {l}{z=1+i}{a=|z-3|}{text{Solvefor}btext{where}}{b=a}

$$\left. \begin{array} { l } { z = 1 + i }\\ { a = | z - 3 | }\\ { \text{Solve for } b \text{ where} } \\ { b = a } \end{array} \right.$$

Solve for z, a, b

$$b=\sqrt{5}\approx 2.236067977$$

Solution Steps

Consider the second equation. Insert the known values of variables into the equation.

$$a=|1+i-3|$$

Subtract 3 from 1+i to get -2+i.

$$a=|-2+i|$$

The modulus of a complex number a+bi is \sqrt{a^{2}+b^{2}}. The modulus of -2+i is \sqrt{5}.

$$a=\sqrt{5}$$

Consider the third equation. Insert the known values of variables into the equation.

$$b=\sqrt{5}$$

The system is now solved.

$$z=1+i a=\sqrt{5} b=\sqrt{5}$$