Which of the following is/are true? (1) (1+i)n = 2n2(sinnπ4+icosnπ4)

1.	Which of the following is/are true? (1) (1+i)n = 2n2(sinnπ4+icosnπ4) If (1+i)n = nC0 + nC1i - nC2 - nC3i + nC4............... (2) nC0 - nC2 + nC4 - nC6................ = 2n2 sinnπ4 (3) nC1 - nC3 + nC5 - nC7....................= 2n2cosnπ4
Answer» Which of the following is/are true? (1) $(1 + i)^{n}$ = $2^{\frac{n}{2}}$ $(s i n \frac{n π}{4} + i c o s \frac{n π}{4})$ If $(1 + i)^{n}$ = $^{n} C_{0}$ + $^{n} C_{1}$ i - $^{n} C_{2}$ - $^{n} C_{3}$ i + $^{n} C_{4}$ ............... (2) $^{n} C_{0}$ - $^{n} C_{2}$ + $^{n} C_{4}$ - $^{n} C_{6}$ ................ = $2^{\frac{n}{2}}$ $s i n \frac{n π}{4}$ (3) $^{n} C_{1}$ - $^{n} C_{3}$ + $^{n} C_{5}$ - $^{n} C_{7}$ ....................= $2^{\frac{n}{2}} c o s \frac{n π}{4}$

Which of the following is/are true? (1) (1+i)n = 2n2(sinnπ4+icosnπ4) If (1+i)n = nC0 + nC1i - nC2 - nC3i + nC4............... (2) nC0 - nC2 + nC4 - nC6................ = 2n2 sinnπ4 (3) nC1 - nC3 + nC5 - nC7....................= 2n2cosnπ4

Answer»

Which of the following is/are true?

(1) $(1 + i)^{n}$ = $2^{\frac{n}{2}}$ $(s i n \frac{n π}{4} + i c o s \frac{n π}{4})$

If $(1 + i)^{n}$ = $^{n} C_{0}$ + $^{n} C_{1}$ i - $^{n} C_{2}$ - $^{n} C_{3}$ i + $^{n} C_{4}$ ...............

(2) $^{n} C_{0}$ - $^{n} C_{2}$ + $^{n} C_{4}$ - $^{n} C_{6}$ ................ = $2^{\frac{n}{2}}$ $s i n \frac{n π}{4}$

(3) $^{n} C_{1}$ - $^{n} C_{3}$ + $^{n} C_{5}$ - $^{n} C_{7}$ ....................= $2^{\frac{n}{2}} c o s \frac{n π}{4}$