# Roots of Complex Numbers

The roots of complex numbers are a fundamental concept in mathematics, bridging the gap between algebra and geometry. Complex numbers, comprising a real part and an imaginary part, possess unique properties when it comes to finding their roots. Understanding the roots of complex numbers involves delving into the intricate realm of complex analysis, where principles such as De Moivre's theorem and polar representation play crucial roles. These roots not only have applications in pure mathematics but also find extensive use in various fields including physics, engineering, and signal processing, making them indispensable in both theoretical and practical contexts.

Questions

- What is the root of #x^3 - x - 1 = 0# in exact form?
- How do you find all the real and complex roots of # x^6 - 4x^5 - 24x^2 + 10x - 3 = 0#?
- The value of C99 is =?
- How do you find all solutions to #x^4-i=0#?
- Can you find the solutions of the equation: # \qquad qquad \qquad x^2 + i x - i \ = \ 0 \ "?" # Make sure to give your answers in standard complex form ( a + bi form).
- How do you find all solutions to #x^3+64i=0#?
- How do you solve #6x^2-5x+3=0#?
- How do you find the square root of #16(cos60^@+isin60^@)#?
- What's the function whose roots are #2i (m2), 4-i, and i\sqrt 3#?
- How do you simplify #\frac { \root[ 3] { x ^ { 2} y ^ { 7} } } { \root [ 6] { x y ^ { 2} } }#?
- Find all the complex solutions of the equation #x^6 + 64 = 0#?
- Write in terms of I √-64?
- What roots of #z^4+z^2+1 = 0# satisfy #abs(z) < 1# ?
- The product of #(root5 8)##(root3 16)# can be expressed as #2^n#. What is the value of #n#?
- One solution of #x^3+(2-i)x^2+(-4-3i)x+(1+i)=0# is #x=1+i#. Find the only positive real solution for #x#?
- Show that #f# has at least one root in #RR# ?
- Show that x=#1/4# is one of the roots of equation 4#x^3#-#x^2#-4x+1=0 Factorise 4#x^3#-#x^2#-4x+1 completely. Hence,solve (pls see below).?
- If the ratio of the roots of #lx^2+nx+n = 0# is #p/q# then how do you prove that #(p/q)^(1/2)+(q/p)^(1/2)-(n/l)^(1/2) = 0# ?
- What is the modulus of #6 + 7i#?
- Difference between roots and factors of an equation?