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Complex numbers
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A complex number is a number of the form z = a +bi, where a and b are real numbers and i = sqrt{-1}. The number a is called the real part of z, and the number b is called the imaginary part of z. If
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Complex numbers
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Find the values of x and y that make the equation true: 2x – 7 + (3 – y)i = -4 + 6i.
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Complex numbers
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Evaluate (2|underline{35^o})^5 and write the answer in exponential form.
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Complex numbers
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Let z 3 = 1 i . Use De Moivre’s Theorem to solve for z . The cube roots of the equation in polar form are given by: (a) z 0 = cos ( 6 ) + i sin ( 6 ) , z 1 = cos ( 5 6 ) + i sin ( 5 6 ) , z 2 = cos ( 3 6 ) + i sin ( 3 6 ) (b) z 0 = cos
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Complex numbers
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Simplify (1 + i)^{12} and leave your final answer in cartesian/rectangular form.
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Complex numbers
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Find the three complex solutions of the equation z^3-8i=0, and write them in the standard form a+bi.
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Complex numbers
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Calculate and write the quotient (4 – i)/(3 + 2i) in the a + bi form.
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