What is 3cis(pi/4)*sqrt(5)cis(pi/2) ?

The solution to 3cis(pi/4)*sqrt(5)cis(pi/2) is (3sqrt(5)pi^2i^2c^2s^2)/8

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simplify 3cis(pi/4)*sqrt(5)cis(pi/2)

simplify

3 c i s (\frac{π}{4}) \cdot 5 c i s (\frac{π}{2})

\frac{3 5 π ^{2} i ^{2} c ^{2} s ^{2}}{8}

Solution steps

3 c i s (\frac{π}{4}) 5 c i s (\frac{π}{2})

Apply exponent rule:

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

ii = i^{1 + 1}

= 3 cs \frac{π}{4} 5 c i^{1 + 1} s \frac{π}{2}

Add the numbers:

1 + 1 = 2

= 3 cs \frac{π}{4} 5 c i^{2} s \frac{π}{2}

Apply exponent rule:

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

cc = c^{1 + 1}

= 3 s \frac{π}{4} 5 c^{1 + 1} i^{2} s \frac{π}{2}

Add the numbers:

1 + 1 = 2

= 3 s \frac{π}{4} 5 c^{2} i^{2} s \frac{π}{2}

Apply exponent rule:

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

ss = s^{1 + 1}

= 3 \cdot \frac{π}{4} 5 c^{2} i^{2} s^{1 + 1} \frac{π}{2}

Add the numbers:

1 + 1 = 2

= 3 \cdot \frac{π}{4} 5 c^{2} i^{2} s^{2} \frac{π}{2}

Multiply fractions:

a \cdot \frac{b}{c} \cdot \frac{d}{e} = \frac{a \cdot b \cdot d}{c \cdot e}

= \frac{ππ 3 5 c ^{2} i ^{2} s ^{2}}{4 \cdot 2}

ππ 35 c^{2} i^{2} s^{2} = 35 π^{2} i^{2} c^{2} s^{2}

= \frac{3 5 π ^{2} i ^{2} c ^{2} s ^{2}}{4 \cdot 2}

Multiply the numbers:

4 \cdot 2 = 8

= \frac{3 5 π ^{2} i ^{2} c ^{2} s ^{2}}{8}

t^{3} e^{- 2 t} sinh (4 t)

(5 r - 3)^{3}

e^{- l n (\frac{y}{x})}

- 4 X^{3} Y^{2 \circ} 5 X^{6} Y^{- 2 \circ} (- 8 X Y Z)

(- 8 - \frac{1}{10}) \cdot (- 10)

What is 3cis(pi/4)*sqrt(5)cis(pi/2) ?
The solution to 3cis(pi/4)*sqrt(5)cis(pi/2) is (3sqrt(5)pi^2i^2c^2s^2)/8