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Question

If Z= (135i)(49i) find z6


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Solution

Rationalize the complex number by multiplying and dividing by 4+9i

135i49i × 4+9i4+9i = 5220i+117i45i216i281

=97+97i97= (1+i)

In polar form

z=2 (cosπ4+isinπ4)

z6 = [2(cosπ4+isinπ4)]6

(2)6[(cosπ4+isinπ4)]6

z6= 8[cos 3π2 + isin3π2]

=8[0-i] = -8i


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