As per the given question, Let I = = = = = = = = =
Integrate the function in 
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Miscellaneous Exercise
Integrate the function in
If, then find the least positive integral value of m.
Solution:- Along these lines, the most un-positive number is \[1.\] Thus, the most un-positive necessary worth of \[m\text{ }is\text{ }4\text{ }\left( =\text{ }4\text{ }\times \text{ }1...
If ![\[\left( a~+~ib \right)\text{ }\left( c~+~id \right)\text{ }\left( e~+~if \right)\text{ }\left( g~+~ih \right)\text{ }=\text{ }\mathbf{A}\text{ }+~i\mathbf{B}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-8cae9017141f4305164470a3e7d32c5b_l3.png "Rendered by QuickLaTeX.com")
then show that ![\[\left( {{a}^{\mathbf{2}}}~+~{{b}^{\mathbf{2}}} \right)\text{ }\left( {{c}^{\mathbf{2}}}~+~{{d}^{\mathbf{2}}} \right)\text{ }\left( {{e}^{\mathbf{2}}}~+~{{f}^{\mathbf{2}}} \right)\text{ }\left( {{g}^{\mathbf{2}}}~+~{{h}^{\mathbf{2}}} \right)\text{ }=\text{ }{{\mathbf{A}}^{\mathbf{2}}}~+\text{ }{{\mathbf{B}}^{\mathbf{2}}}.\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-0bf71d0242806b7da3aa96f5a9770837_l3.png "Rendered by QuickLaTeX.com")
According to the given question, the solution should be
Find the number of non-zero integral solutions of the equation ![\[~{{\left| \mathbf{1}\text{ }-\text{ }\mathbf{i} \right|}^{\mathbf{x}}}~=\text{ }{{\mathbf{2}}^{\mathbf{x}}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-226cc557eaa336622d38a48d68c451a9_l3.png "Rendered by QuickLaTeX.com")
Thus, \[0\]is the main necessary arrangement of the given condition. Thus, the quantity of non-zero necessary arrangements of the given condition is \[0.\]
If α and β are different complex numbers with |β| = 1, then find
Solution:- According to the given question, the solution should be
If ![\[{{\left( x~+~iy \right)}^{\mathbf{3}}}~=~u~+~iv,~\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-d67ebc4d4c1269d2d2b61aa13ce5fcb9_l3.png "Rendered by QuickLaTeX.com")
, then show that
Solution:- According to the given question, the solution should be
Find the modulus of
Solution:- According to the given question, the solution should be
Find the real numbers x and y if (x – iy) (3 + 5i) is the conjugate of – 6 – 24i.
Let’s suppose \[z\text{ }=\text{ }\left( x-iy \right)\text{ }\left( 3\text{ }+\text{ }5i \right)\] And \[\left( 3x\text{ }+\text{ }5y \right)\text{ }~i\left( 5x\text{ }-\text{ }3y \right)\text{...
Find the modulus and argument of the complex number
Solution:- According to the given question, the solution should be
Let ![\[{{\mathbf{z}}_{\mathbf{1}}}~=\text{ }\mathbf{2}\text{ }-i,\text{ }{{\mathbf{z}}_{\mathbf{2}}}~=\text{ }-\mathbf{2}\text{ }+~i.\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-363911d17b2c9708c2dd4f7da58a2b68_l3.png "Rendered by QuickLaTeX.com")
, find
(i) , (ii) Solution:- According to the given question, the solution should be
Solve:
Solution:- According to the given question, the solution should be
If ![\[{{\mathbf{z}}_{\mathbf{1}}}~=\text{ }\mathbf{2}\text{ }~i,\text{ }{{\mathbf{z}}_{\mathbf{2}}}~=\text{ }\mathbf{1}\text{ }+~i,\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-3e8dcbe2120945f1e83c89511c87221a_l3.png "Rendered by QuickLaTeX.com")
,Find
Solution:- According to the question, the solution should be Given,\[\text{ }{{z}_{1}}~=\text{ }2\text{ }-i,\text{ }{{z}_{2}}~=\text{ }1\text{ }+~i\]
Solve the following equation: ![\[21{{x}^{2}}-\text{ }28x~+\text{ }10\text{ }=\text{ }0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-79450961eb6663f727540264fd62e8bd_l3.png "Rendered by QuickLaTeX.com")
Given quadratic condition, \[21{{x}^{2}}-\text{ }28x~+\text{ }10\text{ }=\text{ }0\] On contrasting it and \[a{{x}^{2}}~+~bx~+~c~=\text{ }0,~\]we get \[a~=\text{ }21,~b~=-\text{ }28,\text{...
Solve the following equation: ![\[27{{x}^{2}}-\text{ }10x~+\text{ }1\text{ }=\text{ }0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-c786037e982243d9716298610666c5da_l3.png "Rendered by QuickLaTeX.com")
Given quadratic condition, \[27{{x}^{2}}-\text{ }10x~+\text{ }1\text{ }=\text{ }0\] On contrasting it and\[a{{x}^{2}}~+~bx~+~c~=\text{ }0\], we get \[a~=\text{ }27,~b~=-\text{ }10,\text{...
Solve the following equation : ![\[{{x}^{2}}-\text{ }2x\text{ }+\text{ }3/2\text{ }=\text{ }0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-57ad207a5bc1f6cea5dc6ffd56fbfc3e_l3.png "Rendered by QuickLaTeX.com")
Given quadratic condition, \[{{x}^{2}}-\text{ }2x\text{ }+\text{ }3/2\text{ }=\text{ }0\] It very well may be re-composed as: \[~2{{x}^{2}}-\text{ }4x\text{ }+\text{ }3\text{ }=\text{ }0\] On...
Solve the following equation : ![\[~\mathbf{3}{{\mathbf{x}}^{\mathbf{2}}}-\text{ }\mathbf{4x}\text{ }+\text{ }\mathbf{20}/\mathbf{3}\text{ }=\text{ }\mathbf{0}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-940defe49c1a90f6d12289ea840d4a84_l3.png "Rendered by QuickLaTeX.com")
Given quadratic condition, \[\mathbf{3}{{\mathbf{x}}^{\mathbf{2}}}-\text{ }\mathbf{4x}\text{ }+\text{ }\mathbf{20}/\mathbf{3}\text{ }=\text{ }\mathbf{0}\] It very well may be re-composed as:...
Convert the following in the polar form:
(I) (ii) Solution:- According to the given question, the solution should be,
Solve the following:
Solution:- According to the given question, the solution should be,
Reduce to the standard form
Solution:- According to the given question, the solution should be,
For any two complex numbers z1 and z2, prove that Re (z1z2) = Re z1 Re z2 – Im z1 Im z2
Solution:- According to the given question, the solution should be,
Evaluate:
Solution:- According to the given question, the solution should be