polar(2+2i) — step-by-step solution

Compute the polar representation of

2 + 2 i

as module * exp(i * argument)

The modulus of the complex number

a + i b

\sqrt{a^{2} + b^{2}}

thus:

\sqrt{2^{2} + 2^{2}}

\sqrt{4 + 4}

\sqrt{8}

2 \times \sqrt{2}

Argument(a + ib) is the angle (in radians) from the positive real axis: 0, Pi, ±Pi/2, atan(b/a) or atan(b/a) + Pi (case depends on a and b):

atan (\frac{2}{2})

atan (1)

\frac{π}{4}

Final polar form:

2 \times \sqrt{2} \times \exp (i \times \frac{π}{4})

2 \times \sqrt{2} \times \exp (\frac{i π}{4})

▷Result: $2 \exp (\frac{i π}{4}) \times \sqrt{2}$