यदि (a + ib)(c + id)(e + if)(g + ih) = A + iB हो, तब ({a^2} + {b^2})({c^2} + {d^2})({e

English

Gujarati

Hindi

4-1.Complex numbers

medium

यदि $(a + ib)(c + id)(e + if)(g + ih)$$ = A + iB$ हो, तब $({a^2} + {b^2})({c^2} + {d^2})({e^2} + {f^2})({g^2} + {h^2})$ का मान है

A

${A^2} + {B^2}$

B

${A^2} - {B^2}$

C

${A^2}$

D

${B^2}$

Solution

(a) $(a + ib)(c + id)(e + if)(g + ih) = A + iB$ …….$(i)$

$⇒ (a – ib)(c – id)(e – if)(g – ih) = A – iB$ ……$(ii)$

$(i) $ व $(ii) $ का गुणा करने पर

$({a^2} + {b^2})({c^2} + {d^2})({e^2} + {f^2})({g^2} + {h^2}) = {A^2} + {B^2}$

Standard 11

Mathematics

Share

Similar Questions

$\frac{{{i^{592}} + {i^{590}} + {i^{588}} + {i^{586}} + {i^{584}}}}{{{i^{582}} + {i^{580}} + {i^{578}} + {i^{576}} + {i^{574}}}} – 1$ का मान है

medium

निम्नलिखित व्यंजक को $a+i b$ के रूप में व्यक्त कीजिए

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

medium

यदि $\,\left| \begin{array}{l}\,6i\,\,\,\,\, – 3i\,\,\,\,\,\,\,\,\,1\\\,\,4\,\,\,\,\,\,\,\,\,3i\,\,\,\,\,\, – 1\\\,20\,\,\,\,\,\,\,\,3\,\,\,\,\,\,\,\,\,\,i\end{array} \right|\,$=$x + iy$, तो $(x, y) =$

easy

$x^{2}+x+1=0$ को हल कीजिए।

easy

यदि ${i^2} = – 1$, तो $\sum\limits_{n = 1}^{200} {{i^n}} $का मान है

easy