If ( 3 + i ) 100 = 2 99 ( p + i q ) , then p and q are roots of the equation :

Step-by-step solution

( 3 + i ) 100 = 2 99 ( p + i q ) 2 100 cos π 6 + i sin π 6 100 = 2 99 p + i q 2 100 e i 50 π 3 = 2 99 p + i q 2 cos 50 π 3 + i sin 50 π 3 = p + i q 2 cos 17 π - π 3 + i sin 17 π - π 3 = p + i q 2 - cos π 3 + i sin π 3 = p + i q 2 - 1 2 + i 3 2 = p + i q p = - 1   &   q = 3 p and q Roots of the equation x 2 - ( 3 - 1 ) x - 3 = 0