Mathematics

Eleven Standard

Test your understanding of this lesson Complex number | An important illustration:-

1)
The standard form of \((1-2i)^{-3}\) is
  • -11-2i
  • -11+2i
  • \(\frac{-11-2i}{25}\)
  • \(\frac{-11}{25}-\frac{2i}{25}\)
2)
The standard form of \(\frac{1}{4+3i}\) is
  • \(\frac{4-3i}{25}\)
  • \(\frac{4+3i}{25}\)
  • \(\frac{4}{25}-\frac{3i}{25}\)
  • \(\frac{4}{25}+\frac{3i}{25}\)
3)
If \(A+Bi=\frac{3+2i\sin\theta}{1-2i\sin\theta}\) then A =
  • \(\frac{3-4\sin\theta}{1-4\sin^{2}\theta}\)
  • \(\frac{3-4\sin\theta}{1+4\sin^{2}\theta}\)
  • \(\frac{3+4\sin\theta}{1+4\sin^{2}\theta}\)
  • \(\frac{3+4\sin\theta}{1-4\sin^{2}\theta}\)
4)
If Z= \(\frac{(1-i)^{2}}{2+i}\) then Im(z)=
  • \(\frac{4}{5}\)
  • \(\frac{4i}{5}\)
  • -\(\frac{4}{5}\)
  • -\(\frac{4i}{5}\)
5)
If \(z_{1}=1+i\) and \(z_{2}=-2+4i\) then Im\((\frac{z_{1}z_{2}}{\overline{z_{2}}})\)=
  • \(\frac{1}{5}+\frac{7i}{5}\)
  • \(\frac{1}{5}-\frac{7i}{5}\)
  • -\(\frac{1}{5}-\frac{7i}{5}\)
  • -\(\frac{1}{5}+\frac{7i}{5}\)

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