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Popular Word Problems >

What is the product of 3sqrt(6)cis((pi)/8) and 2sqrt(5)cis((7pi)/6)?

Solution

Wha t i s t h e p ro d u c t o f 36 c i s (\frac{π}{8}) an d 25 c i s (\frac{7 π}{6}) ?

Solution

\frac{7 30 π ^{2} i ^{2} c ^{2} s ^{2}}{8}

Solution steps

(36 c i s (\frac{π}{8})) (25 c i s (\frac{7 π}{6}))

Remove parentheses:

(a) = a

= 36 c i s \frac{π}{8} \cdot 25 c i s \frac{7 π}{6}

Multiply fractions:

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

= \frac{π 7 π 3 6 c i s \cdot 2 5 c i s}{8 \cdot 6}

π 7 π 36 c i s \cdot 25 c i s = 4265 π^{2} i^{2} c^{2} s^{2}

= \frac{42 6 5 π ^{2} i ^{2} c ^{2} s ^{2}}{8 \cdot 6}

Multiply the numbers:

8 \cdot 6 = 48

= \frac{42 6 5 π ^{2} i ^{2} c ^{2} s ^{2}}{48}

Cancel the common factor:

6

= \frac{7 6 5 π ^{2} i ^{2} c ^{2} s ^{2}}{8}

Factor

6 : 23

Factor

8 : 2^{3}

= \frac{7 2 3 5 π ^{2} i ^{2} c ^{2} s ^{2}}{2 ^{3}}

Cancel

\frac{7 2 3 5 π ^{2} i ^{2} c ^{2} s ^{2}}{2 ^{3}} : \frac{7 3 5 π ^{2} i ^{2} c ^{2} s ^{2}}{2 ^{\frac{5}{2}}}

= \frac{7 3 5 π ^{2} i ^{2} c ^{2} s ^{2}}{2 ^{\frac{5}{2}}}

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

= \frac{7 3 5 π ^{2} i ^{2} c ^{2} s ^{2}}{2 ^{2} 2}

Simplify

735 π^{2} i^{2} c^{2} s^{2} : 715 π^{2} i^{2} c^{2} s^{2}

= \frac{7 15 π ^{2} i ^{2} c ^{2} s ^{2}}{2 ^{2} 2}

2^{2} = 4

= \frac{7 15 π ^{2} i ^{2} c ^{2} s ^{2}}{4 2}

Rationalize

\frac{7 15 π ^{2} i ^{2} c ^{2} s ^{2}}{4 2} : \frac{7 30 π ^{2} i ^{2} c ^{2} s ^{2}}{8}

= \frac{7 30 π ^{2} i ^{2} c ^{2} s ^{2}}{8}

Popular Examples

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