Solve -3(-4+i)^2-3(-4+1)+1=

$$- 3 ( - 4 + i ) ^ { 2 } - 3 ( - 4 + 1 ) + 1 =$$

Evaluate

$$-35+24i$$

Solution Steps

Calculate -4+i to the power of 2 and get 15-8i.

$$-3\left(15-8i\right)-3\left(-4+1\right)+1$$

Multiply -3 and 15-8i to get -45+24i.

$$-45+24i-3\left(-4+1\right)+1$$

Add -4 and 1 to get -3.

$$-45+24i-3\left(-3\right)+1$$

Multiply 3 and -3 to get -9.

$$-45+24i-\left(-9\right)+1$$

The opposite of -9 is 9.

$$-45+24i+9+1$$

Add -45+24i and 9 to get -36+24i.

$$-36+24i+1$$

Add -36+24i and 1 to get -35+24i.

$$-35+24i$$

Real Part

$$-35$$

Solution Steps

Calculate -4+i to the power of 2 and get 15-8i.

$$Re(-3\left(15-8i\right)-3\left(-4+1\right)+1)$$

Multiply -3 and 15-8i to get -45+24i.

$$Re(-45+24i-3\left(-4+1\right)+1)$$

Add -4 and 1 to get -3.

$$Re(-45+24i-3\left(-3\right)+1)$$

Multiply 3 and -3 to get -9.

$$Re(-45+24i-\left(-9\right)+1)$$

The opposite of -9 is 9.

$$Re(-45+24i+9+1)$$

Add -45+24i and 9 to get -36+24i.

$$Re(-36+24i+1)$$

Add -36+24i and 1 to get -35+24i.

$$Re(-35+24i)$$

The real part of -35+24i is -35.

$$-35$$