Solve 3-2texttt{i}*(-4+3texttt{i})

$$3-2 \texttt{i} \times (-4+3 \texttt{i} )$$

Evaluate

$$9+8i$$

Solution Steps

Multiply 2i times -4+3i.

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

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

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

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

$$3-\left(-6-8i\right)$$

The opposite of -6-8i is 6+8i.

$$3+\left(6+8i\right)$$

Combine the real and imaginary parts in numbers 3 and 6+8i.

$$3+6+8i$$

Add 3 to 6.

$$9+8i$$

Real Part

$$9$$

Solution Steps

Multiply 2i times -4+3i.

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

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

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

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

$$Re(3-\left(-6-8i\right))$$

The opposite of -6-8i is 6+8i.

$$Re(3+\left(6+8i\right))$$

Combine the real and imaginary parts in numbers 3 and 6+8i.

$$Re(3+6+8i)$$

Add 3 to 6.

$$Re(9+8i)$$

The real part of 9+8i is 9.

$$9$$