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Find √i+√-i

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Find √i+√-i
  • 1 answers

Rishu Mathematician 6 years, 8 months ago

Solve:

 {tex} √i+√(-i){/tex}

{tex}=√(e^(i π/2) )+√(〖-e〗^(i π/2) ){/tex}

{tex}=〖e〗^(i π/4)+ie^(i π/4){/tex}

{tex}=〖e〗^(i π/4) (1+i){/tex}

{tex}=〖e〗^(i π/4) (√2 e^(i π/4)){/tex}

{tex}=√2 e^(i π/2){/tex}

{tex}=i√2{/tex}

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