Polar Form of Complex Numbers — Quiz

Question 6 • Precalculus

What is the rectangular form of 17 times open paren cosine of open paren 315 degrees close paren plus i sine open paren 315 degrees close paren close paren ?

Answer

the fraction with numerator 17 square root of 2 and denominator 2 plus the fraction with numerator 17 square root of 2 and denominator 2 i

negative the fraction with numerator 17 square root of 2 and denominator 2 plus the fraction with numerator 17 square root of 2 and denominator 2 i

negative the fraction with numerator 17 square root of 2 and denominator 2 minus the fraction with numerator 17 square root of 2 and denominator 2 i

the fraction with numerator 17 square root of 2 and denominator 2 minus the fraction with numerator 17 square root of 2 and denominator 2 i

Explanation

At 315°, the reference angle is 45°, and the angle is in the fourth quadrant, where cosine is positive and sine is negative. Thus cos(315°) = √2/2 and sin(315°) = −√2/2. Multiplying each by 17 gives 17√2/2 − (17√2/2)i, which is choice B.

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