Solve 11+2i/4-i=x

$$\frac { 11 + 2 i } { 4 - i } = x$$

Solve for x

$$x=\frac{42}{17}+\frac{19}{17}i\approx 2.470588235+1.117647059i$$

Steps for Solving Linear Equation

Multiply both numerator and denominator of \frac{11+2i}{4-i} by the complex conjugate of the denominator, 4+i.

$$\frac{\left(11+2i\right)\left(4+i\right)}{\left(4-i\right)\left(4+i\right)}=x$$

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

$$\frac{\left(11+2i\right)\left(4+i\right)}{4^{2}-i^{2}}=x$$

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

$$\frac{\left(11+2i\right)\left(4+i\right)}{17}=x$$

Multiply complex numbers 11+2i and 4+i like you multiply binomials.

$$\frac{11\times 4+11i+2i\times 4+2i^{2}}{17}=x$$

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

$$\frac{11\times 4+11i+2i\times 4+2\left(-1\right)}{17}=x$$

Do the multiplications in 11\times 4+11i+2i\times 4+2\left(-1\right).

$$\frac{44+11i+8i-2}{17}=x$$

Combine the real and imaginary parts in 44+11i+8i-2.

$$\frac{44-2+\left(11+8\right)i}{17}=x$$

Do the additions in 44-2+\left(11+8\right)i.

$$\frac{42+19i}{17}=x$$

Divide 42+19i by 17 to get \frac{42}{17}+\frac{19}{17}i.

$$\frac{42}{17}+\frac{19}{17}i=x$$

Swap sides so that all variable terms are on the left hand side.

$$x=\frac{42}{17}+\frac{19}{17}i$$