Algebra

Polar Coordinates

Polar Coordinates - Complex Numbers

         

The complex number 8+8i8+8i can be expressed in polar form as a2(cosb+isinb),a\sqrt{2}(\cos b ^\circ+i\sin b ^\circ), where 0<b<1800 < b < 180. What is the value of a+ba+b?

Let PP be the point in the complex plane that corresponds to complex number zz and let OO be the origin. If z=332\vert z \vert = 33 \sqrt{2} and the angle between the line segment OPOP and the positive real axis is π4, \frac{\pi}{4}, then zz can be expressed as a+bi,a+bi, where aa and bb are real numbers. What is the value of a+b?a+b?

Details and assumptions

ii is the imaginary number satisfying i2=1i^2 = -1.

Let PP be the point in the complex plane that corresponds to complex number z,z, and let OO be the origin. If z=12\vert z \vert = 12 and the angle between the line segment OPOP and the positive real axis is πb, \frac{\pi}{b}, then zz can be expressed as a+12i,a+12i, where aa and bb are positive integers. What is a+b?a+b?

Details and assumptions

ii is the imaginary number satisfying i2=1i^2 = -1.

Let OO be the origin on the complex plane, and let PP be the point representing the complex number z=8+64i z = 8 + 64i. If θ\theta is the angle formed by the line segment OPOP and the positive part of the real axis of the complex plane, what is the value of tanθ?\tan \theta?

Details and assumptions

ii is the imaginary unit, where i2=1i^2=-1.

Let PP be the point in the complex plane that corresponds to complex number zz and let OO be the origin. If z=252\vert z \vert = 25 \sqrt{2} and the angle between the line segment OPOP and the positive real axis is π4, \frac{\pi}{4}, then zz can be expressed as a+bi,a+bi, where aa and bb are real numbers. What is the value of a+b?a+b?

Details and assumptions

ii is the imaginary number satisfying i2=1i^2 = -1.

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