QUESTION 1 1.1 Express \( \sqrt{49}+\sqrt{-4}+\sqrt{-64} \) in the form of: \( a \pm b i \) 1.2 Simplify the following complex numbers withou calculator. Write the answer in standard form: 1.2.1 \( -\left(2 i^{3}-3\right)-\left(i^{3}-7\right) \) 1.2.2 \( \frac{5 i^{2}+3 i-2 i^{25}}{5 i^{14}} \) 1.2.3 \( 2 j\left(4+2 j^{5}\right)\left(3-j^{4}\right) \) 1.2.4 \( \frac{6+2 i}{3-2 i} \)

First additional information: The square root of a negative number introduces the imaginary unit \(i\), where \(i=\sqrt{-1}\). This concept dates back to the 16th century when mathematicians like Gerolamo Cardano first explored complex numbers, revolutionizing mathematics. Understanding how to deal with imaginary units is crucial in various areas, including electrical engineering and quantum physics, where they help describe oscillations and wave functions. Second additional information: To really grasp complex numbers, consider their real-world applications. Engineers often use them when analyzing alternating current circuits, which can fluctuate sinusoidally. Similarly, in signal processing, complex numbers aid in representing and manipulating waves and frequencies, making them indispensable in technology today. Understanding the interplay between real and imaginary components enhances problem-solving capacities in these fields!