Download App

Complex Numbers(p-1) — Maths (commerce) STD 11 Commerce / Arts — Question

Maharashtra BoardEnglish MediumSTD 11 Commerce / ArtsMaths (commerce)Complex Numbers(p-1)1 Mark
Question
Evaluate the following : $i^{30}+i^{40}+i^{50}+i^{60}$
✓

Answer

$i^{30}+i^{40}+i^{50}+i^{60}$
$
\begin{aligned}
& =\left(i^4\right)^7 i^2+\left(i^4\right)^{10}+\left(i^4\right)^{12} i^2+\left(i^4\right)^{15} \\
& =(1)^7(-1)+(1)^{10}+(1)^{12}(-1)+(1)^{15} \\
& =-1+1-1+1 \\
& =0
\end{aligned}
$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the following Question.(1 Marks)" from Complex Numbers(p-1)→Complex Numbers(p-1) — all question types→Maths (commerce) STD 11 Commerce / Arts question papers→Maharashtra Board STD 11 Commerce / Arts question papers→Maharashtra Board question paper generator→

Similar questions

Evaluate:(8 – 6)!
→
Heena Enterprise sold cosmetics worth $₹ 25,000$ to Leena traders, a retailer. Leena Traders sold it further to Meena Beauty Products for ₹ 30,000. Meena Beauty Product sold it further to the customers for ₹ 40,000 . The rate of GST is $18 \%$. Find: CGST and SGST
→
Evaluate the following : $\mathrm{i}^{888}$
→
For what values of $x, \frac{4}{3}, x, \frac{4}{27}$ are in G. P.?
→
If $f(x)=2 x^2+3, g(x)=5 x-2$, then find : gog
→
A coin is tossed 8 times. In how many ways can we obtain: at least 6 heads?
→
Find n, if: $\frac{(15-n) !}{(13-n) !}=12$
→
Simplify the following and express in the form $a+i b$ : $\frac{4+3 i}{1-i}$
→
Find the number of diagonals of an $n$-sided polygon. In particular, find the number of diagonals when: $\mathrm{n}=12$
→
A fair die is thrown two times. Find the chance that: both the times die to show the same number (doublet).
→