Simplifying ( √(3) #160; + i)^6 . #10; #10; ( √(3) #160; #10;+ i)^6 = ( ( √(3) #160; + i)^3)^2 #10; #10; = ( ( √(3))^3 + i^3 #10 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Complex Numbers

Simplify: √...

Question

Simplify: $(\sqrt{3} + i)^{6}$

Open in App

Solution

Simplifying ${(\sqrt{3} + i)}^{6}$ .

${(\sqrt{3} + i)}^{6} = {({(\sqrt{3} + i)}^{3})}^{2}$

$= ({(\sqrt{3})}^{3} + i^{3} + 3 {(\sqrt{3})}^{2} i + 3 (\sqrt{3}) {(i)}^{2})$

$= {(3 \sqrt{3} - i + 9 i - 3 \sqrt{3})}^{2}$

$= {(8 i)}^{2}$

$= - 64$

Suggest Corrections

Similar questions

\frac{(\sqrt{3} - i)^{6}}{(1 + i)^{8}}

i^{2} + i^{4} + i^{6} + . . . + (2 n + 1)

\frac{(\sqrt{3} - i)^{6}}{(1 + i)^{8}}

\frac{i {(\sqrt{3 + i})}^{6}}{4 {(1 - i \sqrt{3})}^{2}}

(1 + i)^{6} + (1 - i)^{6}

Join BYJU'S Learning Program