Solve (6-sqrt{-1})+(4-6sqrt{-1})-(14-sqrt{-49})

$$(6- \sqrt{ -1 } )+(4-6 \sqrt{ -1 } )-(14- \sqrt{ -49 } )$$

Evaluate (complex solution)

$$-4$$

Solution Steps

Calculate the square root of -1 and get i.

$$6-i+4-6\sqrt{-1}-\left(14-\sqrt{-49}\right)$$

Combine the real and imaginary parts in 6-i+4.

$$-6\sqrt{-1}+6+4-i-\left(14-\sqrt{-49}\right)$$

Add 6 to 4.

$$-6\sqrt{-1}+10-i-\left(14-\sqrt{-49}\right)$$

Calculate the square root of -49 and get 7i.

$$-6\sqrt{-1}+10-i-\left(14-7i\right)$$

Calculate the square root of -1 and get i.

$$-6i+10-i-\left(14-7i\right)$$

Combine the real and imaginary parts in -6i+10-i.

$$10+\left(-6-1\right)i-\left(14-7i\right)$$

Add -6 to -1.

$$10-7i-\left(14-7i\right)$$

Subtract 14-7i from 10-7i by subtracting corresponding real and imaginary parts.

$$10-14+\left(-7-\left(-7\right)\right)i$$

Subtract 14 from 10. Subtract -7 from -7.

$$-4$$

Real Part (complex solution)

$$-4$$

Solution Steps

Calculate the square root of -1 and get i.

$$Re(6-i+4-6\sqrt{-1}-\left(14-\sqrt{-49}\right))$$

Combine the real and imaginary parts in 6-i+4.

$$Re(-6\sqrt{-1}+6+4-i-\left(14-\sqrt{-49}\right))$$

Add 6 to 4.

$$Re(-6\sqrt{-1}+10-i-\left(14-\sqrt{-49}\right))$$

Calculate the square root of -49 and get 7i.

$$Re(-6\sqrt{-1}+10-i-\left(14-7i\right))$$

Calculate the square root of -1 and get i.

$$Re(-6i+10-i-\left(14-7i\right))$$

Combine the real and imaginary parts in -6i+10-i.

$$Re(10+\left(-6-1\right)i-\left(14-7i\right))$$

Add -6 to -1.

$$Re(10-7i-\left(14-7i\right))$$

Subtract 14-7i from 10-7i by subtracting corresponding real and imaginary parts.

$$Re(10-14+\left(-7-\left(-7\right)\right)i)$$

Subtract 14 from 10. Subtract -7 from -7.

$$Re(-4)$$

The real part of -4 is -4.

$$-4$$

Evaluate

$$\text{Indeterminate}$$