Please answer the 63rd Q 63 If z = 4 + 3i, then z4 - 16z3 + - Maths - Complex Numbers and Quadratic Equations

Question

Please answer the 63rd Q

63   If   z   =   4   +   3 i ,
  then   z 4   -   16 z 3   +   114 z
2   -   400 z   +   630   is

(1) 0 (2) 5
(3) - 5 (4) 625

Lovina Kansal · Accepted Answer

Dear student
Given: z=4+3i⇒z2=4+3i2=16-9+24i=7+24iNow, z3=z×z2=4+3i7+24i=28+96i+21i-72=117i-44and z4=z22=7+24i2=49-576+336iConsider, z4-16z3+114z2-400z+630=49-576+336i-16117i-44+1147+24i-4004+3i+630=49-576+336i-1872i+704+798+2736i-1600-1200i+630=5
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Please answer the 63rd Q. 63 . If z = 4 + 3 i , then z 4 - 16 z 3 + 114 z 2 - 400 z + 630 is (1) 0 (2) 5 (3) - 5 (4) 625

Please answer the 63rd Q.

$63 . If z = 4 + 3 i, then z^{4} - 16 z^{3} + 114 z^{2} - 400 z + 630 is$

(1) 0 (2) 5
(3) $- 5$ (4) 625