Solve (2+5i)(2*5i)

$$( 2 + 5 i ) ( 2 \cdot 5 i )$$

Evaluate

$$-50+20i$$

Solution Steps

Multiply 2+5i times 2.

$$\left(2\times 2+5i\times 2\right)\times \left(5i\right)$$

Do the multiplications.

$$\left(4+10i\right)\times \left(5i\right)$$

Multiply 4+10i times 5i.

$$4\times \left(5i\right)+10\times 5i^{2}$$

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

$$4\times \left(5i\right)+10\times 5\left(-1\right)$$

Do the multiplications. Reorder the terms.

$$-50+20i$$

Real Part

$$-50$$

Solution Steps

Multiply 2+5i times 2.

$$Re(\left(2\times 2+5i\times 2\right)\times \left(5i\right))$$

Do the multiplications in 2\times 2+5i\times 2.

$$Re(\left(4+10i\right)\times \left(5i\right))$$

Multiply 4+10i times 5i.

$$Re(4\times \left(5i\right)+10\times 5i^{2})$$

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

$$Re(4\times \left(5i\right)+10\times 5\left(-1\right))$$

Do the multiplications in 4\times \left(5i\right)+10\times 5\left(-1\right). Reorder the terms.

$$Re(-50+20i)$$

The real part of -50+20i is -50.

$$-50$$