Question

i 1947+i 1950 complex number​

Answer 1

$\textbf{Given:}$

$\mathrm{i^{1947}+i^{1950}}$

$\textbf{To find:}$

$\text{Simplified form of}$

$\mathrm{i^{1947}+i^{1950}}$

$\textbf{Solution:}$

$\text{Concept used:}$

$\mathrm{i=\sqrt{-1}}$

$\mathrm{i^2=-1}$

$\mathrm{i^3=-i}$

$\mathrm{i^4=1}$

$\text{Consider,}$

$\mathrm{i^{1947}+i^{1950}}$

$\text{Split the power interms of multiple of 4}$

$\mathrm{=i^{1944}\;i^3+i^{1948}\;i^2}$

$\mathrm{=i^{1944}(-i)+i^{1948}(-1)}$

$\mathrm{=(i^4)^{486}(-i)+(i^4)^{487}(-1)}$

$\mathrm{=(1)^{486}(-i)+(1)^{487}(-1)}$

$\mathrm{=(1)(-i)+(1)(-1)}$

$\mathrm{=-i-1}$

$\mathrm{=-1-i}$

$\textbf{Answer:}$

$\text{The simplified form is -1-i}$

Find more:

If a-bi/a+bi=1+i/1-i then,prove a+b=0

https://brainly.in/question/14173316

Express the complex number z = 5+i/2+3i in the form a + ib

https://brainly.in/question/6695271

Find the square root of -12+6i

https://brainly.in/question/17692861