AMU MCA Complex Number Previous Year Questions (PYQs)
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Showing 9 questions
A real value of $x$ will satisfy the equation $\left(\dfrac{3 - 4ix}{3 + 4ix}\right)=\alpha - i\beta; (\alpha,\beta \text{ are real}),$ if
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If $\omega$ is a complex cube root of unity, then the value of
$\dfrac{p + q\omega + r\omega^2}{r + p\omega + q\omega^2} + \dfrac{p + q\omega + r\omega^2}{q + r\omega + p\omega^2}$ $(p,q,r \in R)$ is equal to
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If $P, Q, R, S$ are represented by the complex numbers $4+i, 1+6i, -4+3i, -1-2i$ respectively, then $PQRS$ is a
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If $n$ is a positive integer, then $(1+i)^n + (1-i)^n$ is equal to
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The amplitude of the complex number $1+\sin\alpha-i\cos\alpha$ is
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The points $z_1=x+iy$ and $z_2=\frac{1}{-x+iy}$ in the complex plane lie on
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The ring $Z[\sqrt{3}] = {a + b\sqrt{3} ; a,b \in Z}$
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$Z[\sqrt{3}]$ has no zero divisors and is closed under addition and multiplication, hence it is an integral domain.
The value of $\sum_{n=1}^{13}(i^n + i^{n+1})$, where $i=\sqrt{-1}$ equals
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Solution
$i^n$ repeats every 4 terms
Pair terms cancel ⇒ sum reduces to $i-1$
Final Answer: $\boxed{i-1}$
The value of $\left(\frac{1+i}{1-i}\right)^{100}$ is equal to
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Solution
$\frac{1+i}{1-i} = i$
So expression = $i^{100} = (i^4)^{25} = 1$
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