What is expand (1+j)e^{(jpit)/2} ?

The solution to expand (1+j)e^{(jpit)/2} is e^{(pijt)/2}+je^{(pijt)/2}

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expand (1+j)e^{(jpit)/2}

expand

(1 + j) e^{\frac{jπ t}{2}}

e^{\frac{πj t}{2}} + j e^{\frac{πj t}{2}}

Solution steps

(1 + j) e^{\frac{jπ t}{2}}

= e^{\frac{πj t}{2}} (1 + j)

Apply the distributive law:

a (b + c) = ab + a c

a = e^{\frac{jπ t}{2}}, b = 1, c = j

= e^{\frac{jπ t}{2}} \cdot 1 + e^{\frac{jπ t}{2}} j

= 1 \cdot e^{\frac{πj t}{2}} + j e^{\frac{πj t}{2}}

Multiply:

1 \cdot e^{\frac{πj t}{2}} = e^{\frac{πj t}{2}}

= e^{\frac{πj t}{2}} + j e^{\frac{πj t}{2}}

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What is expand (1+j)e^{(jpit)/2} ?
The solution to expand (1+j)e^{(jpit)/2} is e^{(pijt)/2}+je^{(pijt)/2}