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Popular >

simplify (1+i)/(1-i^{41)}

Solution

simplify

\frac{1 + i}{1 - i ^{41}}

Solution

i

Solution steps

\frac{1 + i}{1 - i ^{41}}

1 - i^{41} = 1 - i

= \frac{1 + i}{1 - i}

Apply complex arithmetic rule:

\frac{a + bi}{c + d i} = \frac{( c - d i ) ( a + bi )}{( c - d i ) ( c + d i )} = \frac{( a c + b d ) + ( b c - a d ) i}{c ^{2} + d ^{2}}

a = 1, b = 1, c = 1, d = - 1

= \frac{( 1 \cdot 1 + 1 \cdot ( - 1 ) ) + ( 1 \cdot 1 - 1 \cdot ( - 1 ) ) i}{1 ^{2} + ( - 1 ) ^{2}}

Refine

= \frac{2 i}{2}

Simplify

\frac{2 i}{2} : i

= i

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Frequently Asked Questions (FAQ)

What is (1+i)/(1-i^{41)} ?
The solution to (1+i)/(1-i^{41)} is i