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

Simplify the following:

Question 1.

i^{1947} + i^{1950}

Solution:

Question 2.

i^{1948} – i^{-1869}

Solution:

Question3.

\(\sum_{n=1}^{12} i^{n}\)

Solution:

Question 4.

\(i^{59}+\frac{1}{i^{59}}\)

Solution:

Question 5.

i i^{2} i^{3} …….. i^{2000}

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.

∴ i^{135} = i^{3} = -i

(ii) The remainder is 3 when 19 is divided by 4.

∴ i^{19} = i^{3} = -i

(iii) We have, i^{999} = 1/i^{999}

On dividing 999 by 4, we obtain 3 as the remainder.

(iv)

Question 2.

Show that:

Solution:

Question 3.

Solution: