The process of identifying all complex number solutions entails deciphering equations in which the unknown variable is a complex number. These complex numbers take the form a + bi, wherein 'a' represents the real component, 'b' signifies the imaginary component, and 'i' stands for the square root of -1. The solutions to these equations may contain real and/or imaginary elements.
| Topic | Problem | Solution |
|---|---|---|
| None | Simplify, if possible. \[ \sqrt{-12} \] \[ \sqrt{… | The square root of a negative number is not a real number, but it can be expressed as a complex num… |
| None | Determine whether the complex number is a solutio… | To determine if a complex number is a solution to the equation, we can substitute the complex numbe… |
| None | Which choice is equivalent to the expression belo… | The square root of a negative number is an imaginary number. |
| None | b) $3 i^{2}-8 i-7=0$ | We are given the quadratic equation in complex numbers: \(3 i^{2}-8 i-7=0\). |
| None | a) $i^{2}+2 i+9=0$ | Given the equation \(i^{2}+2 i+9=0\). This is a quadratic equation in the complex number \(i\). The… |
| None | c) $3 i^{2}-14 i+16=0$ | Given the quadratic equation in complex numbers: \(3 i^{2}-14 i+16=0\) |
| None | a) $i^{2}+i-30=0$ | Given the equation \(i^{2}+i-30=0\). This is a quadratic equation in the complex number \(i\). |
| None | (1) $\mathrm{i}^{4 \mathrm{n}+3}$ (2) $i^{8 n+85}… | The problem is asking for the value of \(i^{4n+3}\), where \(i\) is the imaginary unit and \(n\) is… |
| None | $2.25-11 j-7.75+1.5 j=0.5 j-1$ | Combine real and imaginary parts: \(-9.5j - 5.5 = 0.5j - 1\) |