A Nice Algebra Equation • X=?

In todays video, I will be teaching you how to solve an interesting problem. Make sure to like, subscribe, and also comment any questions or video ideas you may have relating to math!
#maths #exponents #mathematics #mathstricks #mathchallenge #algebra #equation #problem #challenge #Olympiad #MathOlympiad

[@roger7341]

Nice problem to illustrate the application of Euler's equation: Find four 4th roots of -4 or of 4(-1)=4e^(iπ+i2jπ),j=0,1,2,3
x_j=√2e^(iπ/4+ijπ/2)=√2[cos(π/4+jπ/2)+i*sin(π/4+jπ/2)],j=0,1,2,3
x_0=√2(√2/2+i√2/2)=1+i; x_1=√2(-√2/2+i√2/2)=-1+i; x_2=√2(-√2/2-i√2/2)=-1-i; x_3=√2(√2/2-i√2/2)=1-i;