Algebra

Complex Numbers

Complex Numbers Arithmetic

         

What is the absolute value of the complex number 12+5i?12+5i?

Details and assumptions

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

Is it true that ((z))=((z))\Re\big(\Im(z)\big) = \Im\big(\Re(z)\big) for all complex numbers z?z?

What is the value of (9+81)(20400)? \left(9 + \sqrt{-81}\right)\left(20 - \sqrt{-400}\right)?

Simplify 4+2i2i\frac{4+2i}{2-i}.

Details and assumptions
ii is the imaginary number that satisfies i2=1i^2 = -1.

Which set of complex numbers satisfy the equation iz+z=0iz + \overline{z} = 0?

Hint: Start by letting z=x+iyz = x + iy.

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