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Advanced Math/Complex numbers - polar form

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Expert: - 7/26/2009


Question
I'm studying CIE "A Level" Mathematics and the topic Complex number. I know the formula for modulus is ((x^2)+(y^2))^.5 & argument =tan-1(y/x) but I still can't get the correct answers. Please help me. The complex number w is given by w=-1/2 + i(3^1/2)/2. Find the modulus & argument of w. Many Thanks

Answer

Modulus
Questioner: Warm
Country: China
Category: Advanced Math
Private: No
Subject: Complex no.
Question: I'm studying CIE "A Level" Mathematics and the topic Complex number. I know the formula for modulus is ((x^2)+(y^2))^.5 & argument =tan-1(y/x) but I still can't get the correct answers. Please help me. The complex number w is given by w=-1/2 + i(3^1/2)/2. Find the modulus & argument of w. Many Thanks

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w= - 1/2 + i sqrt(3)/2

See picture.

The modulus is 2 and the argument is 60 degrees or pi/3.  Review your stuff about the 30-60-90 triangle.

Paul Klarreich

Expertise

I can answer questions in basic to advanced algebra (theory of equations, complex numbers), precalculus (functions, graphs, exponential, logarithmic, and trigonometric functions and identities), basic probability, and finite mathematics, including mathematical induction. I can also try (but not guarantee) to answer questions on Abstract Algebra -- groups, rings, etc. and Analysis -- sequences, limits, continuity. I won't understand specialized engineering or business jargon.

Experience

I taught at a two-year college for 25 years, including all subjects from algebra to third-semester calculus.

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