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:
Samacheer Kalvi 12th Maths Solutions Chapter 2 Complex Numbers Ex 2.1 Q1

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

Question 2.
i1948 – i-1869
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 2 Complex Numbers Ex 2.1 Q2

Question3.
\(\sum_{n=1}^{12} i^{n}\)
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 2 Complex Numbers Ex 2.1 Q3

Question 4.
\(i^{59}+\frac{1}{i^{59}}\)
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 2 Complex Numbers Ex 2.1 Q4

Question 5.
i i2 i3 …….. i2000
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 2 Complex Numbers Ex 2.1 Q5

Question 6.
\(\sum_{n=1}^{10} i^{n+50}\)
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 2 Complex Numbers Ex 2.1 Q6

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

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

Question 1.
Evaluate the following:
Samacheer Kalvi 12th Maths Solutions Chapter 2 Complex Numbers Ex 2.1 1
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.
Samacheer Kalvi 12th Maths Solutions Chapter 2 Complex Numbers Ex 2.1 2

(iv) Samacheer Kalvi 12th Maths Solutions Chapter 2 Complex Numbers Ex 2.1 3

Question 2.
Show that:
Samacheer Kalvi 12th Maths Solutions Chapter 2 Complex Numbers Ex 2.1 4
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 2 Complex Numbers Ex 2.1 5
Samacheer Kalvi 12th Maths Solutions Chapter 2 Complex Numbers Ex 2.1 6

 

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

Question 3.
Samacheer Kalvi 12th Maths Solutions Chapter 2 Complex Numbers Ex 2.1 7
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 2 Complex Numbers Ex 2.1 8

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