Express -3 - -22-3-i in the form a-ib and find a-

The correct option is B 6+2√(6) ( √(3) + √(2))(2√(3) i) = √(3)(2√(3) i) + √(2)(2√(3) i) = 6 + √(3)i +2√(6) √(2)i = ( 6+2√(6)) i ...

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Byju's Answer

Standard XII

Mathematics

Algebra of Complex Numbers

Express -√3...

Question

Express $(- \sqrt{3} + \sqrt{2}) (2 \sqrt{3} - i)$ in the form $a + i b$ and find $a$ .

\sqrt{3} - \sqrt{2}

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- 6 + 2 \sqrt{6}

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\sqrt{3} + \sqrt{2}

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- 6 - 2 \sqrt{6}

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Solution

The correct option is B $- 6 + 2 \sqrt{6}$
$(- \sqrt{3} + \sqrt{2}) (2 \sqrt{3} - i)$
$= - \sqrt{3} (2 \sqrt{3} - i) + \sqrt{2} (2 \sqrt{3} - i)$
$= - 6 + \sqrt{3} i + 2 \sqrt{6} - \sqrt{2} i$
$= (- 6 + 2 \sqrt{6}) - i (\sqrt{2} + \sqrt{3})$

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Similar questions

Q. Simplify and express the answer in the positive exponenet form:
(i)

\frac{(- 3)^{3} \times 2^{6}}{6 \times 2^{3}}

(ii)

\frac{(2^{3})^{5} \times 5^{4}}{4^{3} \times 5^{2}}

Question 6

Which of the following expressions show that rational numbers are associative under multiplication.
(a) $\frac{2}{3} \times (\frac{- 6}{7} \times \frac{3}{5}) = (\frac{2}{3} \times \frac{- 6}{7}) \times \frac{3}{5}$
(b) $\frac{2}{3} \times (\frac{- 6}{7} \times \frac{3}{5}) = \frac{2}{3} \times (\frac{3}{5} \times \frac{- 6}{7})$
(c) $\frac{2}{3} \times (\frac{- 6}{7} \times \frac{3}{5}) = (\frac{3}{5} \times \frac{2}{3}) \times \frac{- 6}{7}$
(d) $(\frac{2}{3} \times \frac{- 6}{7}) \times \frac{3}{5} = (\frac{- 6}{7} \times \frac{2}{3}) \times \frac{3}{5}$

Suppose A is a non-singular matrix such that $A^{3} - 3 A^{2} + 6 A - I = 0. T h e n, A^{- 1}$ =___

Write an algebraic expression for the statement '6 less than the quotient of x and 3 equals 2'.

Question 6

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Express (−√3+√2)(2√3−i) in the form a+ib and find a.

The correct option is B −6+2√6(−√3+√2)(2√3−i)=−√3(2√3−i)+√2(2√3−i)=−6+√3i+2√6−√2i=(−6+2√6)−i(√2+√3)

Express $(- \sqrt{3} + \sqrt{2}) (2 \sqrt{3} - i)$ in the form $a + i b$ and find $a$ .

The correct option is B $- 6 + 2 \sqrt{6}$
$(- \sqrt{3} + \sqrt{2}) (2 \sqrt{3} - i)$
$= - \sqrt{3} (2 \sqrt{3} - i) + \sqrt{2} (2 \sqrt{3} - i)$
$= - 6 + \sqrt{3} i + 2 \sqrt{6} - \sqrt{2} i$
$= (- 6 + 2 \sqrt{6}) - i (\sqrt{2} + \sqrt{3})$