Subjects complex numbers

Complex Expression 08E76B

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1. **State the problem:** Calculate the value of $\sqrt{3,312,400} \times e^{-i \times 130^\circ}$. 2. **Calculate the square root:** $$\sqrt{3,312,400} = 1820$$ 3. **Rewrite the expression:** $$1820 \times e^{-i \times 130^\circ}$$ 4. **Convert the exponential to trigonometric form using Euler's formula:** $$e^{i\theta} = \cos \theta + i \sin \theta$$ So, $$e^{-i \times 130^\circ} = \cos(-130^\circ) + i \sin(-130^\circ) = \cos 130^\circ - i \sin 130^\circ$$ 5. **Calculate cosine and sine values:** $$\cos 130^\circ \approx -0.6428$$ $$\sin 130^\circ \approx 0.7660$$ 6. **Multiply by 1820:** $$1820 \times (-0.6428 - i \times 0.7660) = -1169.1 - 1393.1i$$ **Final answer:** $$\boxed{-1169.1 - 1393.1i}$$