Solve 2sqrt{3}+iquadsqrt{2}quad(4-8i)^2-(-4+8i)^2

$$2 \sqrt { 3 } + i \quad \sqrt { 2 } \quad ( 4 - 8 i ) ^ { 2 } - ( - 4 + 8 i ) ^ { 2 }$$

Evaluate

$$2\left(\sqrt{2}\left(32-24i\right)+\left(24+32i\right)+\sqrt{3}\right)\approx 141.973769607-3.882250994i$$

Solution Steps

Calculate 4-8i to the power of 2 and get -48-64i.

$$2\sqrt{3}+i\sqrt{2}\left(-48-64i\right)-\left(-4+8i\right)^{2}$$

Multiply i and -48-64i to get 64-48i.

$$2\sqrt{3}+\left(64-48i\right)\sqrt{2}-\left(-4+8i\right)^{2}$$

Calculate -4+8i to the power of 2 and get -48-64i.

$$2\sqrt{3}+\left(64-48i\right)\sqrt{2}-\left(-48-64i\right)$$

The opposite of -48-64i is 48+64i.

$$2\sqrt{3}+\left(64-48i\right)\sqrt{2}+\left(48+64i\right)$$

Real Part

$$2 {(\sqrt{3} + 32 \sqrt{2} + 24)} = 141.973769607$$