Solve 5i[1-i]-2[3+4i]=

$$5 i [ 1 - i ] - 2 [ 3 + 4 i ] =$$

Evaluate

$$-1-3i$$

Solution Steps

Multiply 5i times 1-i.

$$5i\times 1+5\left(-1\right)i^{2}-2\left(3+4i\right)$$

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

$$5i\times 1+5\left(-1\right)\left(-1\right)-2\left(3+4i\right)$$

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

$$5+5i-2\left(3+4i\right)$$

Multiply 2 times 3+4i.

$$5+5i-\left(2\times 3+2\times \left(4i\right)\right)$$

Do the multiplications in 2\times 3+2\times \left(4i\right).

$$5+5i-\left(6+8i\right)$$

Subtract 6+8i from 5+5i by subtracting corresponding real and imaginary parts.

$$5-6+\left(5-8\right)i$$

Subtract 6 from 5. Subtract 8 from 5.

$$-1-3i$$

Real Part

$$-1$$

Solution Steps

Multiply 5i times 1-i.

$$Re(5i\times 1+5\left(-1\right)i^{2}-2\left(3+4i\right))$$

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

$$Re(5i\times 1+5\left(-1\right)\left(-1\right)-2\left(3+4i\right))$$

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

$$Re(5+5i-2\left(3+4i\right))$$

Multiply 2 times 3+4i.

$$Re(5+5i-\left(2\times 3+2\times \left(4i\right)\right))$$

Do the multiplications in 2\times 3+2\times \left(4i\right).

$$Re(5+5i-\left(6+8i\right))$$

Subtract 6+8i from 5+5i by subtracting corresponding real and imaginary parts.

$$Re(5-6+\left(5-8\right)i)$$

Subtract 6 from 5. Subtract 8 from 5.

$$Re(-1-3i)$$

The real part of -1-3i is -1.

$$-1$$