Solve z=(3/2-3i)(1/1+i)

$$z = ( \frac { 3 } { 2 - 3 i } ) ( \frac { 1 } { 1 + i } )$$

Solve for z

$$z=\frac{15}{26}+\frac{3}{26}i\approx 0.576923077+0.115384615i$$

Steps for Solving Linear Equation

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

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

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

$$z=\frac{6+9i}{13}\times \frac{1}{1+i}$$

Divide 6+9i by 13 to get \frac{6}{13}+\frac{9}{13}i.

$$z=\left(\frac{6}{13}+\frac{9}{13}i\right)\times \frac{1}{1+i}$$

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

$$z=\left(\frac{6}{13}+\frac{9}{13}i\right)\times \frac{1\left(1-i\right)}{\left(1+i\right)\left(1-i\right)}$$

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

$$z=\left(\frac{6}{13}+\frac{9}{13}i\right)\times \frac{1-i}{2}$$

Divide 1-i by 2 to get \frac{1}{2}-\frac{1}{2}i.

$$z=\left(\frac{6}{13}+\frac{9}{13}i\right)\left(\frac{1}{2}-\frac{1}{2}i\right)$$

Multiply \frac{6}{13}+\frac{9}{13}i and \frac{1}{2}-\frac{1}{2}i to get \frac{15}{26}+\frac{3}{26}i.

$$z=\frac{15}{26}+\frac{3}{26}i$$

Assign z

$$z≔\frac{15}{26}+\frac{3}{26}i$$