Tessa Leach

2022-02-02

Write the complex number $\frac{8}{1+i}$ in standard form?

nebajcioz

Expert

Step 1
In the division of complex number you need first to change the denominator into a pure real number. To do that you multiply and divide by the complex conjugate of the denominator, in this case, $1-i$. So:
$\frac{8}{1+i}×\frac{1-i}{1-i}=\frac{8-8i}{1+1}=\frac{8}{2}-\frac{8}{2}i=4-4i$
Remember that: $\left(1+i\right)\left(1-i\right)=1-i+i-{i}^{2}$ but ${i}^{2}=\sqrt{-1}{\right)}^{2}=-1$
giving: $\left(1+i\right)\left(1-i\right)=1+1=2$

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