Given \[{{a}_{i\text{ }j}}~=\text{ }{{e}^{2ix}}~sin\text{ }x\text{ }j\] Let \[A\text{ }=\text{ }{{[{{a}_{i\text{ }j}}]}_{2\times 2}}\] So, the elements in a \[2\text{ }\times \text{ }2\] matrix are...
Express the following expression in the form of a + ib:
SOLUTION:- According to the given question, the solution should be
Find the multiplicative inverse of the complex numbers – i
How about we think about \[z\text{ }=\text{ }\text{ }I\] Subsequently, the multiplicative backwards of \[\text{ }I\]is given by\[~z-1\]
Find the multiplicative inverse of the complex numbers √5 + 3i
How about we think about \[z\text{ }=\text{ }\surd 5\text{ }+\text{ }3i\] \[{{\left| z \right|}^{2}}~=\text{ }{{\left( \surd 5 \right)}^{2}}~+\text{ }{{3}^{2}}~=\text{ }5\text{ }+\text{ }9\text{...
Find the multiplicative inverse of the complex numbers 4 – 3i
How about we think about \[z\text{ }=\text{ }4\text{ }\text{ }3i\] Then, at that point, \[=\text{ }4\text{ }+\text{ }3i\] And \[{{\left| z \right|}^{2}}~=\text{ }{{4}^{2}}~+\text{ }{{\left( -3...
Express each of the complex number in the form a + ib. (-2 – 1/3i)3
Answer: According to question, the solution should be Hence, \[{{(-2\text{ }\text{ }1/3i)}^{3}}~=\text{ }-22/3\text{ }-\text{ }107/27i\]
Express each of the complex number given in the Exercises 1 to 10 in the form a + ib. (1/3 + 3i)3
According to the question, the solution should be
Express each of the complex number given in the Exercises 1 to 10 in the form a + ib. (1 – i)4
\[{{(1\text{ }~i)}^{4~}}=\text{ }{{[{{(1-\text{ }~i)}^{2}}]}^{2}}\] \[=\text{ }{{[1\text{ }+~{{i}^{2}}~-\text{ }2i]}^{2}}\] \[=\text{ }{{[1\text{ }-\text{ }1\text{ }-\text{...
Express each of the complex number given in the Exercises 1 to 10 in the form a + ib.
SOLUTION:- According to the question, the solution should be
Express each of the complex number given in the Exercises 1 to 10 in the form a + ib.
SOLUTION:- According to question, the solution should be:
Express each of the complex number given in the Exercises 1 to 10 in the form a + ib. (1 – i) – (–1 + i6)
\[\begin{array}{*{35}{l}} \left( 1\text{ }-\text{ }i \right)-\text{ }\text{ }\left( \text{ }1\text{ }+\text{ }i6 \right)\text{ }=\text{ }1\text{ }-\text{ }i\text{ }+\text{ }1\text{ }-\text{ }i6 \\...
Express each of the complex number given in the Exercises 1 to 10 in the form a + ib. 3(7 + i7) + i(7 + i7)
\[3(7\text{ }+~i7)\text{ }+~i(7\text{ }+~i7)~\] \[=\text{ }21\text{ }+~i21\text{ }+~i7\text{ }+~{{i}^{2~}}7\] \[=\text{ }21\text{ }+~i28\text{ }\text{ }7~\] \[[{{i}^{2}}~=\text{ }-1]\] \[=\text{...
Express each of the complex number given in the Exercises 1 to 10 in the form a + ib. i-39
\[{{i}^{-39}}~=\text{ }1/\text{ }{{i}^{39}}~=\text{ }1/\text{ }{{i}^{4\text{ }x\text{ }9\text{ }+\text{ }3}}~\] \[=\text{ }1/\text{ }({{1}^{9}}~x\text{ }{{i}^{3}})\text{ }=\text{ }1/\text{...
Express each of the complex number given in the Exercises 1 to 10 in the form a + ib. i9 + i19
\[{{i}^{9}}~+\text{ }{{i}^{19}}~=\text{ }{{({{i}^{2}})}^{4}}.\text{ }i\text{ }+\text{ }{{({{i}^{2}})}^{9}}.\text{ }i\] \[=\text{ }{{\left( -1 \right)}^{4}}~.\text{ }i\text{ }+\text{ }{{\left( -1...
Express each of the complex number given in the Exercises 1 to 10 in the form a + ib. 1. (5i) (-3/5i)
$(5i)(-3/5i)=5x(-3/5)x{{i}^{2}}$ $=-3x-1[{{i}^{2}}=-1]$ \[=\text{ }3\] Consequently, \[\left( 5i \right)\text{ }\left( -\text{ }3/5i \right)\text{ }=\text{ }3\text{ }+\text{ }i0\]