Solve z=(2-i)(-3+5i)

$$z = ( 2 - i ) ( - 3 + 5 i )$$

Solve for z

$$z=-1+13i$$

Steps for Solving Linear Equation

Multiply complex numbers 2-i and -3+5i like you multiply binomials.

$$z=2\left(-3\right)+2\times \left(5i\right)-i\left(-3\right)-5i^{2}$$

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

$$z=2\left(-3\right)+2\times \left(5i\right)-i\left(-3\right)-5\left(-1\right)$$

Do the multiplications in 2\left(-3\right)+2\times \left(5i\right)-i\left(-3\right)-5\left(-1\right).

$$z=-6+10i+3i+5$$

Combine the real and imaginary parts in -6+10i+3i+5.

$$z=-6+5+\left(10+3\right)i$$

Do the additions in -6+5+\left(10+3\right)i.

$$z=-1+13i$$

Assign z

$$z≔-1+13i$$