It's a problem where you need to know the definitions. Under what conditions on x and y is x+ iy= 0?k3N70n said:Okay.
So far I did this, I don't think there's any basic algebraic errors though it wouldn't be the first time.
[tex](a+bi)^3 + 5(a+bi)^2 = a + bi + 3i[/tex]
[tex]==> (a^3 +3 a^2 bi - 3ab^2-b^3 i) + (5a^2 +10abi-db^2) = a+bi+3i[/tex]
[tex]==> (a^3-3ab^2+5a^2-5b^2-a)+(3a^2b-b^3+10ab-b-3)i=0[/tex]
so somehow I have to use some mathematical magic to make that [itex]i[/itex] dissappear? Is this just a question that I need to play around with algebraically for a while?
Alright Kenton vs the Sidewalk round two
Complex analysis is a branch of mathematics that deals with the study of complex numbers and their functions. It combines the ideas of calculus and algebra to analyze functions of complex variables.
Complex numbers are numbers that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit (defined as the square root of -1). They have both a real and imaginary component.
The basic algebra of complex numbers includes addition, subtraction, multiplication, and division. Addition and subtraction are performed by combining the real and imaginary components separately. Multiplication is done using the distributive property and the fact that i² = -1. Division is done by multiplying the numerator and denominator by the complex conjugate of the denominator.
The main properties of complex numbers include commutativity and associativity of addition and multiplication, distributive property, existence of identity and inverse elements for addition and multiplication, and the fact that every non-zero complex number has a unique multiplicative inverse.
Complex analysis has numerous applications in various fields such as physics, engineering, and economics. It is used to model and analyze systems that involve complex variables, such as electrical circuits, fluid dynamics, and quantum mechanics. It also has applications in signal processing, image processing, and financial analysis.