Solve sqrt{(-9)^2+(-13i)^2}

$$\sqrt { ( - 9 ) ^ { 2 } + ( - 13 i ) ^ { 2 } }$$

Evaluate

$$2\sqrt{22}i\approx 9.38083152i$$

Solution Steps

Calculate -9 to the power of 2 and get 81.

$$\sqrt{81+\left(-13i\right)^{2}}$$

Calculate -13i to the power of 2 and get -169.

$$\sqrt{81-169}$$

Subtract 169 from 81 to get -88.

$$\sqrt{-88}$$

Factor -88=\left(2i\right)^{2}\times 22. Rewrite the square root of the product \sqrt{\left(2i\right)^{2}\times 22} as the product of square roots \sqrt{\left(2i\right)^{2}}\sqrt{22}. Take the square root of \left(2i\right)^{2}.

$$2i\sqrt{22}$$

Real Part

$$0$$