Solve (2-5sqrt{2}i)(3+4sqrt{2}i)=

$$( 2 - 5 \sqrt { 2 } i ) ( 3 + 4 \sqrt { 2 } i ) =$$

Evaluate

$$-7\sqrt{2}i+46\approx 46-9.899494937i$$

Solution Steps

Use the distributive property to multiply 2-5i\sqrt{2} by 3+4i\sqrt{2}.

$$3\left(2-5i\sqrt{2}\right)+4i\left(2-5i\sqrt{2}\right)\sqrt{2}$$

Use the distributive property to multiply 3 by 2-5i\sqrt{2}.

$$6-15i\sqrt{2}+4i\left(2-5i\sqrt{2}\right)\sqrt{2}$$

Use the distributive property to multiply 4i by 2-5i\sqrt{2}.

$$6-15i\sqrt{2}+\left(8i+20\sqrt{2}\right)\sqrt{2}$$

Use the distributive property to multiply 8i+20\sqrt{2} by \sqrt{2}.

$$6-15i\sqrt{2}+8i\sqrt{2}+20\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$6-15i\sqrt{2}+8i\sqrt{2}+20\times 2$$

Multiply 20 and 2 to get 40.

$$6-15i\sqrt{2}+8i\sqrt{2}+40$$

Combine -15i\sqrt{2} and 8i\sqrt{2} to get -7i\sqrt{2}.

$$6-7i\sqrt{2}+40$$

Add 6 and 40 to get 46.

$$46-7i\sqrt{2}$$

Real Part

$$46$$