Express the following expression in the form of a - ib 3-5 i 3-5 i -3-2 i -3-2 i

(3+√(5)i)(3 √(5)i)/(3+√(2)i) (√(3) √(2)i) =(3)^2 (√(5)i)^2/√(3)+√(2)i √(3)+√(2)i =9 5i^2/2√(2)i=9 5/2√(2)i=14/2√(2)i=7/√(2)i =7/√(2)i×i/i=7/√(2)i^2 = 7i/√(2)= 7 ...

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Byju's Answer

Standard XI

Mathematics

Arithmetic Progression

Express the f...

Question

Express the following expression in the form of a + ib

$\frac{(3 + \sqrt{5} i) (3 - \sqrt{5} i)}{(3 + \sqrt{2} i) - (\sqrt{3} - \sqrt{2} i)}$

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Solution

$\frac{(3 + \sqrt{5} i) (3 - \sqrt{5} i)}{(3 + \sqrt{2} i) - (\sqrt{3} - \sqrt{2} i)}$

$= \frac{(3)^{2} - (\sqrt{5} i)^{2}}{\sqrt{3} + \sqrt{2} i - \sqrt{3} + \sqrt{2} i}$

$= \frac{9 - 5 i^{2}}{2 \sqrt{2} i} = \frac{9 - 5}{2 \sqrt{2} i} = \frac{14}{2 \sqrt{2} i} = \frac{7}{\sqrt{2} i}$

$= \frac{7}{\sqrt{2} i} \times \frac{i}{i} = \frac{7}{\sqrt{2} i^{2}} = \frac{- 7 i}{\sqrt{2}} = \frac{- 7 \sqrt{2} i}{2}$

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Express the following expression in the form of a + ib (3+√5i)(3−√5i)(3+√2i)−(√3−√2i)

(3+√5i)(3−√5i)(3+√2i)−(√3−√2i) =(3)2−(√5i)2√3+√2i−√3+√2i =9−5i22√2i=9−52√2i=142√2i=7√2i =7√2i×ii=7√2i2=−7i√2=−7√2i2

Express the following expression in the form of a + ib

$\frac{(3 + \sqrt{5} i) (3 - \sqrt{5} i)}{(3 + \sqrt{2} i) - (\sqrt{3} - \sqrt{2} i)}$