Mathematics

Problem

Let

z_1

and

z_2

be two complex numbers such that

z_1 + z_2 = 5

and

z_1^3 + z_2^3 = 20 + 15i

. Then,

|z_1^4 + z_2^4|

equals (2024 Main, 31 Jan) (a) 75 (b)

25\sqrt{3}

(c)

30\sqrt{3}

(d)

15\sqrt{15}