Class 11Mathematics4-1.Complex numbers Integral power of iota, Algebraic operations and Equality of complex numbers
EasyIf $i = \sqrt{-1}$,then $1 + i^2 + i^3 - i^6 + i^8$ is equal to
- A$2 - i$
- B$1$
- C$3$
- D$-1$
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Similar Questions
Let $z \in \mathbb{C}$ with $\operatorname{Im}(z)=10$ and it satisfies $\frac{2z-n}{2z+n}=2i-1$, where $i=\sqrt{-1}$, for some natural number $n$. Then:
$\text{Re} \left( \frac{(1 + i)^2}{3 - i} \right) =$
Easy
View SolutionExpress the given complex number in the form $a+ib$: $\left[\left(\frac{1}{3}+i \frac{7}{3}\right)+\left(4+i \frac{1}{3}\right)\right]-\left(-\frac{4}{3}+i\right)$
Medium
View SolutionExpress the following in the form of $a+bi$:
$(-5i) \left(\frac{1}{8}i\right)$
$(-5i) \left(\frac{1}{8}i\right)$
Easy
View SolutionIf $m$ and $n$ are respectively the least positive and greatest negative integer values of $k$ such that $\left(\frac{1-i}{1+i}\right)^k = -i$,then $m-n =$
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