Solve (-3+5i)^2+2(-3+5i)+1

$$( - 3 + 5 i ) ^ { 2 } + 2 ( - 3 + 5 i ) + 1$$

Evaluate

$$-21-20i$$

Solution Steps

Calculate -3+5i to the power of 2 and get -16-30i.

$$-16-30i+2\left(-3+5i\right)+1$$

Do the additions.

$$2\left(-3+5i\right)-15-30i$$

Multiply 2 and -3+5i to get -6+10i.

$$-6+10i-15-30i$$

Do the additions.

$$-21-20i$$

Real Part

$$-21$$

Solution Steps

Calculate -3+5i to the power of 2 and get -16-30i.

$$Re(-16-30i+2\left(-3+5i\right)+1)$$

Do the additions in -16-30i+1.

$$Re(2\left(-3+5i\right)-15-30i)$$

Multiply 2 and -3+5i to get -6+10i.

$$Re(-6+10i-15-30i)$$

Do the additions in -6+10i-15-30i.

$$Re(-21-20i)$$

The real part of -21-20i is -21.

$$-21$$