simplify (1-5i)^2

Solution

simplify

(1 - 5 i)^{2}

- 24 - 10 i

Solution steps

(1 - 5 i)^{2}

Apply Perfect Square Formula:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

(1 - 5 i)^{2} = 1^{2} - 2 \cdot 1 \cdot 5 i + (5 i)^{2}

= 1^{2} - 2 \cdot 1 \cdot 5 i + (5 i)^{2}

Simplify

1^{2} - 2 \cdot 1 \cdot 5 i + (5 i)^{2} : - 10 i - 24

= - 10 i - 24

Rewrite in standard complex form:

- 24 - 10 i

= - 24 - 10 i

\frac{- 1 + 5 i}{2 + 3 i}

\frac{39}{10}

20 - (- 5)

9 - (a^{b} + a^{2} + 3) - (a^{b} + 2)