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

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

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

simplify

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

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

Solution steps

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

Apply exponent rule:

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

ii = i^{1 + 1}

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

Add the numbers:

1 + 1 = 2

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

Apply exponent rule:

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

cc = c^{1 + 1}

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

Add the numbers:

1 + 1 = 2

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

Apply exponent rule:

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

ss = s^{1 + 1}

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

Add the numbers:

1 + 1 = 2

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

Multiply fractions:

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

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

π 3 π 2 c^{2} i^{2} s^{2} = 32 π^{2} i^{2} c^{2} s^{2}

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

Multiply the numbers:

2 \cdot 4 = 8

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

Factor

8 : 2^{3}

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

Cancel

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

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

2^{\frac{5}{2}} = 2^{2} 2

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

2^{2} = 4

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

- 4 e^{- 0}

\frac{3 ^{x}}{2 ^{x}}

4 (x - 3)^{2} (x + 2)^{2}

e^{- 4 l n (2)}

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