Solve [-3+2i-4(-2-1)+4(4-3i)]4-3i

$$[ - 3 + 2 i - 4 ( - 2 - 1 ) + 4 ( 4 - 3 i ) ] 4 - 3 i$$

Evaluate

$$100-43i$$

Solution Steps

Subtract 1 from -2 to get -3.

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

Multiply 4 and -3 to get -12.

$$\left(-3+2i-\left(-12\right)+4\left(4-3i\right)\right)\times 4-3i$$

The opposite of -12 is 12.

$$\left(-3+2i+12+4\left(4-3i\right)\right)\times 4-3i$$

Combine the real and imaginary parts in numbers -3+2i and 12.

$$\left(-3+12+2i+4\left(4-3i\right)\right)\times 4-3i$$

Add -3 to 12.

$$\left(9+2i+4\left(4-3i\right)\right)\times 4-3i$$

Multiply 4 times 4-3i.

$$\left(9+2i+4\times 4+4\times \left(-3i\right)\right)\times 4-3i$$

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

$$\left(9+2i+\left(16-12i\right)\right)\times 4-3i$$

Combine the real and imaginary parts in 9+2i+16-12i.

$$\left(9+16+\left(2-12\right)i\right)\times 4-3i$$

Do the additions in 9+16+\left(2-12\right)i.

$$\left(25-10i\right)\times 4-3i$$

Multiply 25-10i times 4.

$$25\times 4-10i\times 4-3i$$

Do the multiplications in 25\times 4-10i\times 4.

$$100-40i-3i$$

Combine the real and imaginary parts.

$$100+\left(-40-3\right)i$$

Add -40 to -3.

$$100-43i$$

Real Part

$$100$$

Solution Steps

Subtract 1 from -2 to get -3.

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

Multiply 4 and -3 to get -12.

$$Re(\left(-3+2i-\left(-12\right)+4\left(4-3i\right)\right)\times 4-3i)$$

The opposite of -12 is 12.

$$Re(\left(-3+2i+12+4\left(4-3i\right)\right)\times 4-3i)$$

Combine the real and imaginary parts in numbers -3+2i and 12.

$$Re(\left(-3+12+2i+4\left(4-3i\right)\right)\times 4-3i)$$

Add -3 to 12.

$$Re(\left(9+2i+4\left(4-3i\right)\right)\times 4-3i)$$

Multiply 4 times 4-3i.

$$Re(\left(9+2i+4\times 4+4\times \left(-3i\right)\right)\times 4-3i)$$

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

$$Re(\left(9+2i+\left(16-12i\right)\right)\times 4-3i)$$

Combine the real and imaginary parts in 9+2i+16-12i.

$$Re(\left(9+16+\left(2-12\right)i\right)\times 4-3i)$$

Do the additions in 9+16+\left(2-12\right)i.

$$Re(\left(25-10i\right)\times 4-3i)$$

Multiply 25-10i times 4.

$$Re(25\times 4-10i\times 4-3i)$$

Do the multiplications in 25\times 4-10i\times 4.

$$Re(100-40i-3i)$$

Combine the real and imaginary parts in 100-40i-3i.

$$Re(100+\left(-40-3\right)i)$$

Add -40 to -3.

$$Re(100-43i)$$

The real part of 100-43i is 100.

$$100$$