$z = i - 1$
Express $z$ in Euler form.

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Solution

$z = i - 1$
Euler form of z is $r e^{i θ}$
when $r = | z | θ = a r y (z)$
$r = \sqrt{1 + 1} = \sqrt{2}$
$θ = {tan}^{- 1} (\frac{1}{- 1}) = π - {tan}^{- 1} (\frac{1}{1})$
$= π - \frac{π}{4}$
$= \frac{3 π}{4}$
So, $r e^{i} = \sqrt{2} e^{i \frac{3 π}{4}}$

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z=i−1Express z in Euler form.

z=i−1Euler form of z is reiθwhen r=|z|θ=ary(z)r=√1+1=√2θ=tan−1(1−1)=π−tan−1(11)=π−π4=3π4So, rei=√2ei3π4

$z = i - 1$
Express $z$ in Euler form.

$z = i - 1$
Euler form of z is $r e^{i θ}$
when $r = | z | θ = a r y (z)$
$r = \sqrt{1 + 1} = \sqrt{2}$
$θ = {tan}^{- 1} (\frac{1}{- 1}) = π - {tan}^{- 1} (\frac{1}{1})$
$= π - \frac{π}{4}$
$= \frac{3 π}{4}$
So, $r e^{i} = \sqrt{2} e^{i \frac{3 π}{4}}$