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Question from Eilis, a student:

How do I solve (1+i) to the power of 2-i?

i.e. (1+i)^(2-i)

Hi Eilis,

You need to use the exponential form to calculate this power. First of all

1 + i = √2 ei(pi/4 + 2n pi)               (1)

for any integer n. Also

1 + i = eln(1 + i)

Thus

(1 + i)2 - i = e (2 - i) ln(1 + i)

Thus using equation (1) the exponent is

(2 - i) ln(1 + i) = (2 - i) [ln(√2) + i(pi/4 + 2npi)]

Expand this expression and simplify.

Penny

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