Solve y=(3-2i)*(1+4i)=

$$y = ( 3 - 2 i ) \cdot ( 1 + 4 i ) =$$

Solve for y

$$y=11+10i$$

Steps for Solving Linear Equation

Multiply complex numbers 3-2i and 1+4i like you multiply binomials.

$$y=3\times 1+3\times \left(4i\right)-2i-2\times 4i^{2}$$

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

$$y=3\times 1+3\times \left(4i\right)-2i-2\times 4\left(-1\right)$$

Do the multiplications in 3\times 1+3\times \left(4i\right)-2i-2\times 4\left(-1\right).

$$y=3+12i-2i+8$$

Combine the real and imaginary parts in 3+12i-2i+8.

$$y=3+8+\left(12-2\right)i$$

Do the additions in 3+8+\left(12-2\right)i.

$$y=11+10i$$

Assign y

$$y≔11+10i$$