simplify (1+4i)^2

Solution

simplify

(1 + 4 i)^{2}

- 15 + 8 i

Solution steps

(1 + 4 i)^{2}

Apply Perfect Square Formula:

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

(1 + 4 i)^{2} = 1^{2} + 2 \cdot 1 \cdot 4 i + (4 i)^{2}

= 1^{2} + 2 \cdot 1 \cdot 4 i + (4 i)^{2}

Simplify

1^{2} + 2 \cdot 1 \cdot 4 i + (4 i)^{2} : 8 i - 15

= 8 i - 15

Rewrite in standard complex form:

- 15 + 8 i

= - 15 + 8 i

\frac{1 + 2}{1 - 2}

x (x + 3) > 0

3 + 2 y = 7

(3 - 1)^{2}

\frac{44}{15} + \frac{17}{2} + \frac{25}{3}