$\frac{( - 1 + i ) ^{2}}{- 5 + i} = \frac{- 1 + 5 i}{13}$

Explanation

Tap the blue circles to see an explanation.

$\frac{( - 1 + i ) ^{2}}{- 5 + i} \overset{◯}{1} \frac{1 - 2 i + i ^{2}}{- 5 + i} \overset{◯}{2} \frac{1 - 2 i - 1}{- 5 + i} \overset{◯}{3} - \frac{2 i}{- 5 + i} \overset{◯}{4} \frac{- 1 + 5 i}{13}$
①	Find $(- 1 + i)^{2}$ in two steps. S1: Change all signs inside bracket. S2: Apply formula $(A - B)^{2} = A^{2} - 2 \cdot A \cdot B + B^{2}$ where $A = 1$ and $B = i$ . $(- 1 + i)^{2} S 1 (1 - i)^{2} S 2 1^{2} - 2 \cdot 1 \cdot i + i^{2} = = 1 - 2 i + i^{2}$
②	$i^{2} = - 1$
③	Simplify numerator $1 - 2 i - 1 = - 2 i$
④	Divide $- 2 i$ by $- 5 + i$ to get $\frac{- 1 + 5 i}{13}$ . ( view steps )

This page was created using

Complex Expression calculator

About the Author

Welcome to MathPortal. This website's owner is mathematician Miloš Petrović. I designed this website and wrote all the calculators, lessons, and formulas.

If you want to contact me, probably have some questions, write me using the contact form or email me on mathhelp@mathportal.org.

Send Me A Comment

Main Navigation

Online Math Calculators

−5+i(−1+i)2​=13−1+5i​

$\frac{( - 1 + i ) ^{2}}{- 5 + i} = \frac{- 1 + 5 i}{13}$