Solve 2/c_{1}=11/2+3i+1/3-2i

$$\frac { 2 } { c _ { 1 } } = \frac { 11 } { 2 + 3 i } + \frac { 1 } { 3 - 2 i }$$

Solve for c_1

$$c_{1}=\frac{25}{61}+\frac{31}{61}i\approx 0.409836066+0.508196721i$$

Steps for Solving Linear Equation

Variable c_{1} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by c_{1}.

$$2=c_{1}\times \frac{11}{2+3i}+c_{1}\times \frac{1}{3-2i}$$

Multiply both numerator and denominator of \frac{11}{2+3i} by the complex conjugate of the denominator, 2-3i.

$$2=c_{1}\times \frac{11\left(2-3i\right)}{\left(2+3i\right)\left(2-3i\right)}+c_{1}\times \frac{1}{3-2i}$$

Do the multiplications in \frac{11\left(2-3i\right)}{\left(2+3i\right)\left(2-3i\right)}.

$$2=c_{1}\times \frac{22-33i}{13}+c_{1}\times \frac{1}{3-2i}$$

Divide 22-33i by 13 to get \frac{22}{13}-\frac{33}{13}i.

$$2=c_{1}\left(\frac{22}{13}-\frac{33}{13}i\right)+c_{1}\times \frac{1}{3-2i}$$

Multiply both numerator and denominator of \frac{1}{3-2i} by the complex conjugate of the denominator, 3+2i.

$$2=c_{1}\left(\frac{22}{13}-\frac{33}{13}i\right)+c_{1}\times \frac{1\left(3+2i\right)}{\left(3-2i\right)\left(3+2i\right)}$$

Do the multiplications in \frac{1\left(3+2i\right)}{\left(3-2i\right)\left(3+2i\right)}.

$$2=c_{1}\left(\frac{22}{13}-\frac{33}{13}i\right)+c_{1}\times \frac{3+2i}{13}$$

Divide 3+2i by 13 to get \frac{3}{13}+\frac{2}{13}i.

$$2=c_{1}\left(\frac{22}{13}-\frac{33}{13}i\right)+c_{1}\left(\frac{3}{13}+\frac{2}{13}i\right)$$

Combine c_{1}\left(\frac{22}{13}-\frac{33}{13}i\right) and c_{1}\left(\frac{3}{13}+\frac{2}{13}i\right) to get \left(\frac{25}{13}-\frac{31}{13}i\right)c_{1}.

$$2=\left(\frac{25}{13}-\frac{31}{13}i\right)c_{1}$$

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

$$\left(\frac{25}{13}-\frac{31}{13}i\right)c_{1}=2$$

Divide both sides by \frac{25}{13}-\frac{31}{13}i.

$$c_{1}=\frac{2}{\frac{25}{13}-\frac{31}{13}i}$$

Multiply both numerator and denominator of \frac{2}{\frac{25}{13}-\frac{31}{13}i} by the complex conjugate of the denominator, \frac{25}{13}+\frac{31}{13}i.

$$c_{1}=\frac{2\left(\frac{25}{13}+\frac{31}{13}i\right)}{\left(\frac{25}{13}-\frac{31}{13}i\right)\left(\frac{25}{13}+\frac{31}{13}i\right)}$$

Do the multiplications in \frac{2\left(\frac{25}{13}+\frac{31}{13}i\right)}{\left(\frac{25}{13}-\frac{31}{13}i\right)\left(\frac{25}{13}+\frac{31}{13}i\right)}.

$$c_{1}=\frac{\frac{50}{13}+\frac{62}{13}i}{\frac{122}{13}}$$

Divide \frac{50}{13}+\frac{62}{13}i by \frac{122}{13} to get \frac{25}{61}+\frac{31}{61}i.

$$c_{1}=\frac{25}{61}+\frac{31}{61}i$$