Solve 1.2+0.7i-2i(-1-i)

$$1.2 + 0.7 i - 2 i ( - 1 - i )$$

Evaluate

$$-0.8+2.7i$$

Solution Steps

Multiply 2i times -1-i.

$$1.2+0.7i-\left(2i\left(-1\right)+2\left(-1\right)i^{2}\right)$$

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

$$1.2+0.7i-\left(2i\left(-1\right)+2\left(-1\right)\left(-1\right)\right)$$

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

$$1.2+0.7i-\left(2-2i\right)$$

Subtract 2-2i from 1.2+0.7i by subtracting corresponding real and imaginary parts.

$$1.2-2+\left(0.7-\left(-2\right)\right)i$$

Subtract 2 from 1.2. Subtract -2 from 0.7.

$$-0.8+2.7i$$

Real Part

$$-0.8$$

Solution Steps

Multiply 2i times -1-i.

$$Re(1.2+0.7i-\left(2i\left(-1\right)+2\left(-1\right)i^{2}\right))$$

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

$$Re(1.2+0.7i-\left(2i\left(-1\right)+2\left(-1\right)\left(-1\right)\right))$$

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

$$Re(1.2+0.7i-\left(2-2i\right))$$

Subtract 2-2i from 1.2+0.7i by subtracting corresponding real and imaginary parts.

$$Re(1.2-2+\left(0.7-\left(-2\right)\right)i)$$

Subtract 2 from 1.2. Subtract -2 from 0.7.

$$Re(-0.8+2.7i)$$

The real part of -0.8+2.7i is -0.8.

$$-0.8$$