simplify (1/t-i)^2

Solution

simplify

(\frac{1}{t} - i)^{2}

(\frac{1}{t ^{2}} - 1) - \frac{2}{t} i

Solution steps

(\frac{1}{t} - i)^{2}

Apply Perfect Square Formula:

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

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

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

Simplify

(\frac{1}{t})^{2} - 2 \cdot \frac{1}{t} i + i^{2} : \frac{1}{t ^{2}} - \frac{2}{t} i - 1

= \frac{1}{t ^{2}} - \frac{2}{t} i - 1

Rewrite in standard complex form:

(\frac{1}{t ^{2}} - 1) - \frac{2}{t} i

= (\frac{1}{t ^{2}} - 1) - \frac{2}{t} i

ln (x^{2} + 1) + (sin (x) + 5)^{4}

\frac{8 ( 6 6 - 5 5 )}{3} - 9

(2 + 32) \cdot 41

\frac{( 1 + b d - b ^{2} ) ( - c + a )}{( d - b ) ( 1 - a c + a ^{2} )}

- 16 (62 - 13)