Solve (7.50)i+37:(1/3)^-1-(-1)^2020+1-11

$$( 7.50 ) i + 37 : ( \frac { 1 } { 3 } ) ^ { - 1 } - ( - 1 ) ^ { 2020 } + 1 - 11$$

Evaluate

$$\frac{4}{3}+7.5i\approx 1.333333333+7.5i$$

Solution Steps

Calculate \frac{1}{3} to the power of -1 and get 3.

$$7.5i+\frac{37}{3}-\left(-1\right)^{2020}+1-11$$

Calculate -1 to the power of 2020 and get 1.

$$7.5i+\frac{37}{3}-1+1-11$$

Do the additions in 7.5i+\frac{37}{3}-1.

$$\frac{34}{3}+\frac{15}{2}i+1-11$$

Do the additions.

$$\frac{4}{3}+\frac{15}{2}i$$

Real Part

$$\frac{4}{3} = 1\frac{1}{3} = 1.3333333333333333$$

Solution Steps

Calculate \frac{1}{3} to the power of -1 and get 3.

$$Re(7.5i+\frac{37}{3}-\left(-1\right)^{2020}+1-11)$$

Calculate -1 to the power of 2020 and get 1.

$$Re(7.5i+\frac{37}{3}-1+1-11)$$

Do the additions in 7.5i+\frac{37}{3}-1.

$$Re(\frac{34}{3}+\frac{15}{2}i+1-11)$$

Do the additions in \frac{34}{3}+7.5i+1-11.

$$Re(\frac{4}{3}+\frac{15}{2}i)$$

The real part of \frac{4}{3}+\frac{15}{2}i is \frac{4}{3}.

$$\frac{4}{3}$$