What is expand 240*(9+8i)/(9.5+8.2i) ?

The solution to expand 240*(9+8i)/(9.5+8.2i) is 230.26223…+3.35259…i

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expand 240*(9+8i)/(9.5+8.2i)

expand

240 \cdot \frac{9 + 8 i}{9.5 + 8.2 i}

230.26223 \dots + 3.35259 \dots i

Solution steps

240 \cdot \frac{9 + 8 i}{9.5 + 8.2 i}

\frac{9 + 8 i}{9.5 + 8.2 i} = \frac{151.1 + 2.2 i}{157.49}

= 240 \cdot \frac{151.1 + 2.2 i}{157.49}

Multiply fractions:

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

= \frac{( 151.1 + 2.2 i ) \cdot 240}{157.49}

Divide the numbers:

\frac{240}{157.49} = 1.52390 \dots

= 1.52390 \dots (151.1 + 2.2 i)

Apply the distributive law:

a (b + c) = ab + a c

a = 1.52390 \dots, b = 151.1, c = 2.2 i

= 1.52390 \dots \cdot 151.1 + 1.52390 \dots \cdot 2.2 i

Simplify

1.52390 \dots \cdot 151.1 + 1.52390 \dots \cdot 2.2 i : 230.26223 \dots + 3.35259 \dots i

= 230.26223 \dots + 3.35259 \dots i

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What is expand 240*(9+8i)/(9.5+8.2i) ?
The solution to expand 240*(9+8i)/(9.5+8.2i) is 230.26223…+3.35259…i