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lostNfound
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I think I got it
Last edited:
LCKurtz said:Start by writing (1+i)n in trigonometric form.
What theorem do you have about raising a complex number in trigonometric form to the nth power?
lostNfound said:I did try putting (1+i)^n in trigonometric form and I got the following:
2^(n/2)*(cos(45*n)+i*sin(45*n))
A complex number is a number that can be written in the form a + bi, where a and b are real numbers and i is the imaginary unit, equal to the square root of -1. Complex numbers are used to represent quantities that do not have a real number solution, such as the square root of a negative number.
Real numbers are numbers that can be represented on a number line, including both positive and negative numbers. Complex numbers, on the other hand, include both real and imaginary components and cannot be plotted on a number line.
To add or subtract complex numbers, you can simply add or subtract the real and imaginary parts separately. For example, to add (3+4i) and (5+2i), you would add 3+5=8 and 4+2=6, resulting in (8+6i).
To multiply complex numbers, you can use the FOIL method, just as you would with binomials. For example, to multiply (3+4i) and (5+2i), you would have (3+4i)(5+2i) = 15+6i+20i+8i^2 = 15+6i+20i-8 = 7+26i. To divide complex numbers, you can perform long division or use the conjugate method.
Complex numbers have many applications in real life, including in engineering, physics, and economics. They are used to model and solve problems that involve alternating currents, resonance, and fluid dynamics, among others. They are also used in the fields of signal processing, control systems, and quantum mechanics.