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Now that you have an efficient way to raise a complex number to an integer power, how can you raise a complex number to a fractional power? Start with a simple case, . The goal is to determine the values of z that make the equation a true statement. These values are the two square roots of i, or . a. Write i in polar form. b. Use De Moivre's Theorem to show that can be written as . c. To solve for z, each side of the equation is raised to the power. Use part (b) to write in polar form. d. Write in rectangular form. Algebraically confirm that . e. The original equation has , so there are two possible values for z. You determined one solution in part (c). Determine the other solution, then graph both solutions.
in polar form
The complex number $0+i$ is in Quadrant I.
Therefore, the polar form of the complex number, $i$ is,
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