Samacheer Kalvi 12th Maths Solutions Chapter 2 Complex Numbers Ex 2.1

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Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 2 Complex Numbers Ex 2.1

Simplify the following:

Question 1.
i¹⁹⁴⁷ + i¹⁹⁵⁰
Solution:

Question 2.
i¹⁹⁴⁸ – i^-1869
Solution:

Question3.
\(\sum_{n=1}^{12} i^{n}\)
Solution:

Question 4.
\(i^{59}+\frac{1}{i^{59}}\)
Solution:

Question 5.
i i² i³ …….. i²⁰⁰⁰
Solution:

Question 6.
\(\sum_{n=1}^{10} i^{n+50}\)
Solution:

Samacheer Kalvi 12th Maths Solutions Chapter 3 Theory of Equations Ex 2.1 Additional Problems

Question 1.
Evaluate the following:

Solution:
135 leaves remainder as 3 when it is divided by 4.
∴ i¹³⁵ = i³ = -i

(ii) The remainder is 3 when 19 is divided by 4.
∴ i¹⁹ = i³ = -i

(iii) We have, i⁹⁹⁹ = 1/i⁹⁹⁹
On dividing 999 by 4, we obtain 3 as the remainder.

(iv)

Question 2.
Show that:

Solution:

 

Question 3.

Solution: