Question

Using Binomial therorm [(2-√7i)^6 ] express in (a+ib )form means complex no. Form .... That's it ​

Answer 1

Answer:

981+i340√7

Step-by-step explanation:

Expand the term using binomial theorem and then add all the complex numbers. This is the final term which we will get.

Or an easier alternate method is as shown

${(2 - \sqrt{7}i) }^{6} \\ {(2 - \sqrt{7}i)}^{3 + 3} \\ {(2 - \sqrt{7}i)}^{3} {(2 - \sqrt{7}i)}^{3} \\ (8 - 12 \sqrt{7} i + 42 {i}^{2} - 7 \sqrt{7} {i}^{3} )(8 - 12 \sqrt{7} i + 42 {i}^{2} - 7 \sqrt{7} {i}^{3} ) \\ (8 - 12 \sqrt{7} i - 42 + 7 \sqrt{7} i)(8 - 12 \sqrt{7} i - 42 + 7 \sqrt{7} i) \\ ( - 34 - 5 \sqrt{7} i)( - 34 - 5 \sqrt{7} i) \\ 1156 + 170 \sqrt{7} i + 170 \sqrt{7} i + 175 {i}^{2} \\ 1156 - 175 + 340 \sqrt{7} i \\ 981 + 340 \sqrt{7} i$