Question

JEE Main Maths Complex Numbers & Quadratic Equations 

$\huge\tt\colorbox{aqua}{Questions}$

Question 1: If (1 + i) (1 + 2i) (1 + 3i) ….. (1 + ni) = a + ib, then what is 2 * 5 * 10….(1 + n2) is equal to?

Question 2: If the cube roots of unity are 1, ω, ω2, then find the roots of the equation (x − 1)3 + 8 = 0.



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Answer 1

Q(1):-)

Given that (1+i)(1+2i)(1+3i)....(1+ni)=α+iβ,

If we take modulus on both sides,

.

.

Squaring both sides,

2.5....(1+n2) = (α2+β2)

Q(2):-)

${ \huge { \pink{ \tt(x−2)^3+8= \: \: \: \: 0  (x−2)^3=−8}}}$

$\huge \tt \green∴ \color{cyan}(x−2)=(−2)(1)^{1/3}$

1,ω,ω²

are cube roots of unity

∴x−2=−2 ∴x=0

OR

x-2=−2ω x=2−2ω

$\orange{ \O \R } \\ \: \: \: \: \: \: x-2 = −2ω²    \: \: \: \: \: \: \: \: \: \:   x=2−2ω²$

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