(1+i)^(2-i) - Math Central

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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 e^{i(/4 + 2n )} (1)

for any integer n. Also

1 + i = e^{ln(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(/4 + 2n)]

Expand this expression and simplify.

Penny

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