Solve frac{-20+isqrt{75}}{40}

$$\frac { - 20 + i \sqrt { 75 } } { 40 }$$

Evaluate

$$\frac{\sqrt{3}i}{8}-\frac{1}{2}\approx -0.5+0.216506351i$$

Solution Steps

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

$$\frac{-20+i\times 5\sqrt{3}}{40}$$

Real Part

$$-\frac{1}{2} = -0.5$$