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Maths Solve the following Question.(1 Marks)

Complex Numbers · Maharashtra Board STD 11 (MSBSHSE - Semi English Medium). 63 questions.

Questions · Page 2 of 2

Solve the following Question.(1 Marks)

Question 511 Mark
Evaluate the following:

$i^{888}$

Answer
We know that, $i^2=-1, i^3=-i, i^4=1$

$\quad i^{888}=\left(i^4\right)^{222}=(1)^{222}=1$

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Question 521 Mark
Evaluate the following:

$i ^{35}$

Answer
We know that, $i^2=-1, i^3=-i, i^4=1$

$\quad i^{35}=\left(i^4\right)^8\left(i^2\right) i=(1)^8(-1) i=-i$

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Question 541 Mark
Write the conjugates of the following complex numbers: cos θ + i sin θ
Answer
Conjugate of (cos θ + i sin θ) is (cos θ – i sin θ)
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Question 551 Mark
Write the conjugates of the following complex numbers: √2 + √3 i
Answer
Conjugate of (√2 + √3 i) is (√2 – √3 i)
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Question 561 Mark
Write the conjugates of the following complex numbers: √5 – i
Answer
Conjugate of (√5 – i) is (√5 + i).
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Question 581 Mark
Write the conjugates of the following complex numbers: -√-5
Answer
.-√-5 = -√5 × √-1 = -√5 i Conjugate of (-√-5) is √5
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Question 591 Mark
Write the conjugates of the following complex numbers: √-5 – √7 i
Answer
Conjugate of (√-5 – √7 i) is (√-5 + √7 i).
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Question 621 Mark
Simplify:
4√-4 + 5√-9 – 3√-16
Answer
$\begin{aligned} & 4 \sqrt{-4}+5 \sqrt{-9}-3 \sqrt{-16} \\ = & 4 \sqrt{4 \times-1}+5 \sqrt{9 \times-1}-3 \sqrt{16 \times-1} \\ = & 4(2 i)+5(3 i)-3(4 i) \\ = & 8 i+15 i-12 i\end{aligned}$

$=11 i$

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Question 631 Mark
Simplify:$\sqrt{-16}+3 \sqrt{-25}+\sqrt{-36}-\sqrt{-625}$
Answer
$\sqrt{-16}+3 \sqrt{-25}+\sqrt{-36}-\sqrt{-625}$
$=\sqrt{16 \times-1}+3 \sqrt{25 \times-1}+\sqrt{36 \times-1}-\sqrt{625 \times-1}$
$= 4i + 3(5i) + 6i – 25i = 25i – 25i = 0$
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