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Covert the complex number `z = 1 + cos (8pi)/(5) + i. sin (8pi)/(5)` in polar form. Find its modulus and argument. |
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Answer» `z = 1 + cos (8pi)/(5) + I sin (8pi)/(5)` `= 2cos^(2)(4pi)/(5) + cos .(4pi)/(5)` `= 2cos.(4pi)/(5)(cos.(4pi)/(5) + isin .(4pi)/(5))` `= - 2cos.(pi)/(5)(-cos.(pi)/(5) + isin .(pi)/(5))` `= 2 cos.(pi)/(5)(cos.(pi)/(5)- isin .(pi)/(5))` `= 2cos.(pi)/(5) (cos(-(pi)/(5)) + isin (-(pi)/(5)))` Thus, `|z| = 2 cos .(pi)/(5) and arg(z) = (pi)/(5)` |
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