2. 919

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Solution

We know that i= −1 .

Therefore,

i 2 =−1

i 3 = i 2 ⋅i =−i

i 4 =1

Given expression is,

i 9 + i 19

By simplifying the above expression, we get

i 9 + i 19 = i 4×2 ⋅i+ i 4×4 ⋅ i 3 =i+( −i ) =0 =0+i⋅0

Thus, in the form of a+ib , the expression can be written as 0+i⋅0 .

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Similar questions

Q. Later she paid Rs 919 to the junk collectors. When she sold the junk she got these notes and coins from Dinu.

Now you make a record in her diary.
Find out how much she earned this time.

Using the given pattern, find the missing numbers.
$1^{2} + 2^{2} + 2^{2} = 3^{2}$
$2^{2} + 3^{2} + 6^{2} = 7^{2}$
$3^{2} + 4^{2} + 12^{2} = 13^{2}$
$4^{2} + 5^{2} + . . .^{2} = 21^{2}$
$5^{2} + . . .^{2} + 30^{2} = 31^{2}$
$6^{2} + 7^{2} + . . . .^{2} = . . . .^{2}$ .

Using the given pattern, find the missing numbers.

1² + 2² + 2² = 3²

2² + 3² + 6² = 7²

3² + 4² + 12² = 13²

4² + 5² + _ ² = 21²

5² + _ ² + 30² = 31²

6² + 7² + _ ² = __²

Question 6
Using the given pattern, find the missing numbers:
$1^{2} + 2^{2} + 2^{2} = 3^{2}$
$2^{2} + 3^{2} + 6^{2} = 7^{2}$
$3^{2} + 4^{2} + 12^{2} = 13^{2}$
$4^{2} + 5^{2} + {- --- -}^{2} = 21^{2}$
$5^{2} + {- --- -}^{2} + 30^{2} = 31^{2}$
$6^{2} + 7^{2} + - --- - 2 = - --- - 2$

Simplify the following:

$9 + 9.01 + 19.019 + 919 + 919.999$

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2. 919

We know that i= −1 . Therefore, i 2 =−1 i 3 = i 2 ⋅i =−i i 4 =1 Given expression is, i 9 + i 19 By simplifying the above expression, we get i 9 + i 19 = i 4×2 ⋅i+ i 4×4 ⋅ i 3 =i+( −i ) =0 =0+i⋅0 Thus, in the form of a+ib , the expression can be written as 0+i⋅0 .

We know that i= −1 .

Therefore,

i 2 =−1

i 3 = i 2 ⋅i =−i

i 4 =1

Given expression is,

i 9 + i 19

By simplifying the above expression, we get

i 9 + i 19 = i 4×2 ⋅i+ i 4×4 ⋅ i 3 =i+( −i ) =0 =0+i⋅0

Thus, in the form of a+ib , the expression can be written as 0+i⋅0 .