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प्रश्न
State True or False for the following:
The order relation is defined on the set of complex numbers.
विकल्प
True
False
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उत्तर
This statement is False.
Explanation:
Comparison of two purely imaginary complex numbers is not possible. However, the two purely real complex numbers can be compared.
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संबंधित प्रश्न
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\[\left( i^{41} + \frac{1}{i^{257}} \right)^9\]
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\[i^{49} + i^{68} + i^{89} + i^{110}\]
Find the value of the following expression:
i49 + i68 + i89 + i110
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i5 + i10 + i15
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\[\frac{1}{(2 + i )^2}\]
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\[\frac{1 - i}{1 + i}\]
Express the following complex number in the standard form a + ib:
\[\frac{(2 + i )^3}{2 + 3i}\]
Express the following complex number in the standard form a + i b:
\[(1 + 2i )^{- 3}\]
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\[(1 + i\sqrt{3} )^2\]
If \[z_1 = 2 - i, z_2 = 1 + i,\text { find } \left| \frac{z_1 + z_2 + 1}{z_1 - z_2 + i} \right|\]
If \[z_1 = 2 - i, z_2 = - 2 + i,\] find
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If \[z_1 = 2 - i, z_2 = - 2 + i,\] find
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Find the smallest positive integer value of m for which \[\frac{(1 + i )^n}{(1 - i )^{n - 2}}\] is a real number.
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Find the number of solutions of \[z^2 + \left| z \right|^2 = 0\].
Express the following complex in the form r(cos θ + i sin θ):
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\[\text { If }z = 1 - \text { cos }\theta + i \text { sin }\theta, \text { then } \left| z \right| =\]
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If \[z = a + ib\] lies in third quadrant, then \[\frac{\bar{z}}{z}\] also lies in third quadrant if
Evaluate the following : i403
State true or false for the following:
If a complex number coincides with its conjugate, then the number must lie on imaginary axis.
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