Solve (3+i)z=10

$$( 3 + i ) z = 10$$

Solve for z

$$z=3-i$$

Steps for Solving Linear Equation

Divide both sides by 3+i.

$$z=\frac{10}{3+i}$$

Multiply both numerator and denominator of \frac{10}{3+i} by the complex conjugate of the denominator, 3-i.

$$z=\frac{10\left(3-i\right)}{\left(3+i\right)\left(3-i\right)}$$

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

$$z=\frac{10\left(3-i\right)}{3^{2}-i^{2}}$$

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

$$z=\frac{10\left(3-i\right)}{10}$$

Multiply 10 times 3-i.

$$z=\frac{10\times 3+10\left(-i\right)}{10}$$

Do the multiplications in 10\times 3+10\left(-i\right).

$$z=\frac{30-10i}{10}$$

Divide 30-10i by 10 to get 3-i.

$$z=3-i$$