Let Z=re^(iθ) ( r0 and π

Question

Let Z=re^(iθ) ( r>0 and π<θ≤3π ) is a root of the equation Z^8-Z^7+Z^6-Z^5+Z^4-Z^3+Z^2-Z+1=0. If the sum of all values of θ is kπ, then k is equal to

MARKS Content Team · Accepted Answer

Correct answer: 16. Given equation is (-Z^9-1)/(-Z-1)=0 ⇒Z^9=-1 where Z≠-1 ⇒Z=e^(i2kπ9), where k=5,6,7,8,10,11,12,13 ⇒ θ=(10π)/9,(12π)/9,(14π)/9,(16π)/9,(20π)/9,(22π)/9,(24π)/9,(26π)/9 ⇒ the sum of all values of θ is equal to 16π ⇒ k=16

Let $Z = r e^{i θ}$ ( $r > 0$ and $π < θ \leq 3 π$ ) is a root of the equation $Z^{8} - Z^{7} + Z^{6} - Z^{5} + Z^{4} - Z^{3} + Z^{2} - Z + 1 = 0 .$ If the sum of all values of $θ$ is $k π$ , then $k$ is equal to

Solution

More Complex Number Questions

Let Z=reiθ ( r>0 and π<θ≤3π ) is a root of the equation Z8-Z7+Z6-Z5+Z4-Z3+Z2-Z+1=0. If the sum of all values of θ is kπ, then k is equal to

Solution

More Complex Number Questions

Let $Z = r e^{i θ}$ ( $r > 0$ and $π < θ \leq 3 π$ ) is a root of the equation $Z^{8} - Z^{7} + Z^{6} - Z^{5} + Z^{4} - Z^{3} + Z^{2} - Z + 1 = 0 .$ If the sum of all values of $θ$ is $k π$ , then $k$ is equal to