Solve (-3+4i)+5(6-3i)-i(1-2i)

$$( - 3 + 4 i ) + 5 ( 6 - 3 i ) - i ( 1 - 2 i )$$

Evaluate

$$25-12i$$

Solution Steps

Multiply 5 times 6-3i.

$$-3+4i+5\times 6+5\times \left(-3i\right)-i\left(1-2i\right)$$

Do the multiplications in 5\times 6+5\times \left(-3i\right).

$$-3+4i+\left(30-15i\right)-i\left(1-2i\right)$$

Combine the real and imaginary parts in -3+4i+30-15i.

$$-3+30+\left(4-15\right)i-i\left(1-2i\right)$$

Do the additions in -3+30+\left(4-15\right)i.

$$27-11i-i\left(1-2i\right)$$

Multiply i times 1-2i.

$$27-11i-\left(i-2i^{2}\right)$$

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

$$27-11i-\left(i-2\left(-1\right)\right)$$

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

$$27-11i-\left(2+i\right)$$

Subtract 2+i from 27-11i by subtracting corresponding real and imaginary parts.

$$27-2+\left(-11-1\right)i$$

Subtract 2 from 27. Subtract 1 from -11.

$$25-12i$$

Real Part

$$25$$

Solution Steps

Multiply 5 times 6-3i.

$$Re(-3+4i+5\times 6+5\times \left(-3i\right)-i\left(1-2i\right))$$

Do the multiplications in 5\times 6+5\times \left(-3i\right).

$$Re(-3+4i+\left(30-15i\right)-i\left(1-2i\right))$$

Combine the real and imaginary parts in -3+4i+30-15i.

$$Re(-3+30+\left(4-15\right)i-i\left(1-2i\right))$$

Do the additions in -3+30+\left(4-15\right)i.

$$Re(27-11i-i\left(1-2i\right))$$

Multiply i times 1-2i.

$$Re(27-11i-\left(i-2i^{2}\right))$$

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

$$Re(27-11i-\left(i-2\left(-1\right)\right))$$

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

$$Re(27-11i-\left(2+i\right))$$

Subtract 2+i from 27-11i by subtracting corresponding real and imaginary parts.

$$Re(27-2+\left(-11-1\right)i)$$

Subtract 2 from 27. Subtract 1 from -11.

$$Re(25-12i)$$

The real part of 25-12i is 25.

$$25$$