Solve (frac{-1+isqrt{3}}{2})^0+(frac{-1-isqrt{3}}{2})^0=

$$( \frac { - 1 + i \sqrt { 3 } } { 2 } ) ^ { 0 } + ( \frac { - 1 - i \sqrt { 3 } } { 2 } ) ^ { 0 } =$$

Evaluate

$$2$$

Solution Steps

To raise \frac{-1+i\sqrt{3}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-1+i\sqrt{3}\right)^{0}}{2^{0}}+\left(\frac{-1-i\sqrt{3}}{2}\right)^{0}$$

To raise \frac{-1-i\sqrt{3}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-1+i\sqrt{3}\right)^{0}}{2^{0}}+\frac{\left(-1-i\sqrt{3}\right)^{0}}{2^{0}}$$

Calculate -1+i\sqrt{3} to the power of 0 and get 1.

$$\frac{1}{2^{0}}+\frac{\left(-1-i\sqrt{3}\right)^{0}}{2^{0}}$$

Calculate 2 to the power of 0 and get 1.

$$\frac{1}{1}+\frac{\left(-1-i\sqrt{3}\right)^{0}}{2^{0}}$$

Anything divided by one gives itself.

$$1+\frac{\left(-1-i\sqrt{3}\right)^{0}}{2^{0}}$$

Calculate -1-i\sqrt{3} to the power of 0 and get 1.

$$1+\frac{1}{2^{0}}$$

Calculate 2 to the power of 0 and get 1.

$$1+\frac{1}{1}$$

Anything divided by one gives itself.

$$1+1$$

Add 1 and 1 to get 2.

$$2$$

Real Part

$$2$$

Solution Steps

To raise \frac{-1+i\sqrt{3}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$Re(\frac{\left(-1+i\sqrt{3}\right)^{0}}{2^{0}}+\left(\frac{-1-i\sqrt{3}}{2}\right)^{0})$$

To raise \frac{-1-i\sqrt{3}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$Re(\frac{\left(-1+i\sqrt{3}\right)^{0}}{2^{0}}+\frac{\left(-1-i\sqrt{3}\right)^{0}}{2^{0}})$$

Calculate -1+i\sqrt{3} to the power of 0 and get 1.

$$Re(\frac{1}{2^{0}}+\frac{\left(-1-i\sqrt{3}\right)^{0}}{2^{0}})$$

Calculate 2 to the power of 0 and get 1.

$$Re(\frac{1}{1}+\frac{\left(-1-i\sqrt{3}\right)^{0}}{2^{0}})$$

Anything divided by one gives itself.

$$Re(1+\frac{\left(-1-i\sqrt{3}\right)^{0}}{2^{0}})$$

Calculate -1-i\sqrt{3} to the power of 0 and get 1.

$$Re(1+\frac{1}{2^{0}})$$

Calculate 2 to the power of 0 and get 1.

$$Re(1+\frac{1}{1})$$

Anything divided by one gives itself.

$$Re(1+1)$$

Add 1 and 1 to get 2.

$$Re(2)$$

The real part of 2 is 2.

$$2$$