Complex Numbers in Mathematics Quiz

Complex number = An element of a number system that extends the real numbers with a specific element denoted i, satisfying the equation $i^2 = -1$ Real part = The real number component in the expression of a complex number $a+bi$ Imaginary part = The imaginary number component in the expression of a complex number $a+bi$ Fundamental theorem of algebra = Asserts that every non-constant polynomial equation with real or complex coefficients has a solution which is a complex number

$(x + 1)^2 = -9$ = The nonreal complex solutions are $-1+3i$ and $-1-3i$ $i^2 = -1$ = The solution is $i$ $(2x - 3)^2 = -16$ = The nonreal complex solutions are $\frac{3}{2} + 2i$ and $\frac{3}{2} - 2i $(y - 4)^2 = -25$ = The nonreal complex solutions are $4+5i$ and $4-5i

Complex numbers allow solutions to all polynomial equations = Even those that have no solutions in real numbers No real number satisfies the equation $i^2 = -1$ = Hence, $i$ was called an imaginary number by René Descartes Complex numbers are regarded as just as 'real' as the real numbers = And are fundamental in many aspects of the scientific description of the natural world The set of complex numbers is denoted by either of the symbols $\mathbb{C}$ or C = Despite the historical nomenclature 'imaginary'

<p>Imaginary unit = Denoted by i and satisfying the equation $i^2 = -1$ Client-side scripting for web applications = Primary usage of JavaScript General-purpose programming = Primary usage of Python Database queries = Primary usage of SQL</p> Signup and view all the answers

<p>$(3x - 7)^2 = -4$ = Real part: $\frac{7}{3}$; Imaginary part: $\pm \frac{\sqrt{4}}{3}i $(4y + 5)^2 = -20$ = Real part: $-\frac{5}{4}$; Imaginary part: $\pm \frac{\sqrt{20}}{4}i $(z + 2)^2 = -12$ = Real part: $-2$; Imaginary part: $\pm \sqrt{12}i $(w - 6)^2 = -36$ = Real part: $6$; Imaginary part: $\pm \sqrt{36}i</p> Signup and view all the answers