1 Use De Moivre's Theorem to find these powers. Express each argument in the range -π < θ ≤ π | |||
a. (2 cis 0.5) 2 | b.( 2 cis )4 | c. (3 cis )2 | d. (5 cis )4 |
2 Find the required roots to solve the following equations and show on an Argand diagram. |
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a. z3 = 8 cis | b. z4 = 9 cis | c. z5 = 32 cis π | d. z6 = 125 cis π |
3 Change these complex numbers to polar form, use De Moivre's Theorem, and leave in rectangular form: | |||
a. (1 + i)4 | b. (√3 + i)5 | c. (4 − 2i)6 | d. (1 + √3i)3 |
4 Solve the following equations: | |||
a. z4 = 25 |
b. z3 = -8 | c. z4 = -100 | d. z3 = -27 |