Finding All Complex Number Solutions

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.

The problems about Finding All Complex Number Solutions

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) $i^{4 n + 3}$ (2) $i^{8 n+85}…	The problem is asking for the value of $i^{4 n + 3}$ , 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: $- 9.5 j - 5.5 = 0.5 j - 1$