Solve -1/2+2i*((3-2/5i)+(-1-i))

$$- \frac { 1 } { 2 } + 2 i \cdot ( ( 3 - \frac { 2 } { 5 } i ) + ( - 1 - i ) )$$

Evaluate

$$\frac{23}{10}+4i=2.3+4i$$

Solution Steps

Combine the real and imaginary parts in numbers 3-\frac{2}{5}i and -1-i.

$$-\frac{1}{2}+2i\left(3-1+\left(-\frac{2}{5}-1\right)i\right)$$

Add 3 to -1. Add -\frac{2}{5} to -1.

$$-\frac{1}{2}+2i\left(2-\frac{7}{5}i\right)$$

Multiply 2i times 2-\frac{7}{5}i.

$$-\frac{1}{2}+2i\times 2+2\left(-\frac{7}{5}\right)i^{2}$$

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

$$-\frac{1}{2}+2i\times 2+2\left(-\frac{7}{5}\right)\left(-1\right)$$

Do the multiplications in 2i\times 2+2\left(-\frac{7}{5}\right)\left(-1\right). Reorder the terms.

$$-\frac{1}{2}+\left(\frac{14}{5}+4i\right)$$

Combine the real and imaginary parts.

$$-\frac{1}{2}+\frac{14}{5}+4i$$

Add -\frac{1}{2} to \frac{14}{5}.

$$\frac{23}{10}+4i$$

Real Part

$$\frac{23}{10} = 2\frac{3}{10} = 2.3$$

Solution Steps

Combine the real and imaginary parts in numbers 3-\frac{2}{5}i and -1-i.

$$Re(-\frac{1}{2}+2i\left(3-1+\left(-\frac{2}{5}-1\right)i\right))$$

Add 3 to -1. Add -\frac{2}{5} to -1.

$$Re(-\frac{1}{2}+2i\left(2-\frac{7}{5}i\right))$$

Multiply 2i times 2-\frac{7}{5}i.

$$Re(-\frac{1}{2}+2i\times 2+2\left(-\frac{7}{5}\right)i^{2})$$

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

$$Re(-\frac{1}{2}+2i\times 2+2\left(-\frac{7}{5}\right)\left(-1\right))$$

Do the multiplications in 2i\times 2+2\left(-\frac{7}{5}\right)\left(-1\right). Reorder the terms.

$$Re(-\frac{1}{2}+\left(\frac{14}{5}+4i\right))$$

Combine the real and imaginary parts in -\frac{1}{2}+\frac{14}{5}+4i.

$$Re(-\frac{1}{2}+\frac{14}{5}+4i)$$

Add -\frac{1}{2} to \frac{14}{5}.

$$Re(\frac{23}{10}+4i)$$

The real part of \frac{23}{10}+4i is \frac{23}{10}.

$$\frac{23}{10}$$