simplify (1+i+t)^2

Solution

simplify

(1 + i + t)^{2}

(t^{2} + 2 t) + (2 + 2 t) i

Solution steps

(1 + i + t)^{2}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

(1 + i + t)^{2} = (1 + i + t) (1 + i + t)

= (1 + i + t) (1 + i + t)

Distribute parentheses

= 1 \cdot 1 + 1 i + 1 \cdot t + i 1 + ii + i t + t \cdot 1 + t i + tt

Simplify

1 \cdot 1 + 1 i + 1 \cdot t + i 1 + ii + i t + t \cdot 1 + t i + tt : 2 i + t^{2} + 2 t + 2 t i

= 2 i + t^{2} + 2 t + 2 t i

Rewrite in standard complex form:

(t^{2} + 2 t) + (2 + 2 t) i

= (t^{2} + 2 t) + (2 + 2 t) i

2 (2 x - 3 = x + 2)

\frac{2 s ^{3} - 5 s ^{2} + 8 s - 14}{( s ^{2} + 4 ) ( s - 1 ) ( s + 1 )}

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(sec (θ) + tan (θ)) cos (θ)

\frac{( x + 2 ) ^{3} ( 9 x - 2 )}{12}