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Find the value of z, if |z |= 4 and arg ...

Find the value of z, if `|z |= 4 and arg (z) = (5pi)/(6)`.

Text Solution

Verified by Experts

Let `z=r(costheta + isintheta) `
Also, `|z| = r= "and" theta = (5pi)/(6)" "[:' arg (z) = theta]`
`:. Z = 4 ["cos"(5pi)/(6)+"isin"(5pi)/(6)]" " [:' z= r (cos theta + isin theta)]`
`= 4 ["cos"(pi(pi)/(6))+"isin"(pi(pi)/(6))]`
`= 4 ["-cos"(pi)/(6)+"isin"(pi)/(6)] `
`= 4 [-sqrt(3)/+i (1)/(2)]=-2sqrt(3)+2i `
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