Multiply complex numbers and find the modulus and polar form

Expand the product using $i^2=-1$:

In polar form $r\angle \theta$, $r$ is the modulus, or distance from zero, and $\theta$ is the angle. For $5+i$:

With DEG selected, the polar result is $\sqrt{26}\angle 11.30993247402$. The second line shows the same result with a decimal radius: $5.09901951359\angle 11.30993247402$. So the modulus is $\sqrt{26}$, about $5.09901951359$, and the angle is about $11.31^{\circ }$. The screen groups long decimals in threes, so $11.30993247402$ is $11.30993247402$.

The chip rewrites the answer already on screen; it does not calculate the line again. Tap it once more to return to $5+i$. Every later answer is written the way the chip shows until you switch it back.

The app stays on, even after a reload. To return to ordinary calculations, open the mode menu and tap the Calculate tile.

• The polar angle is different: check the angle-unit chip. A first-time visitor's calculator starts in RAD. In radians, this example gives $\sqrt{26}\angle \arctan \left(\frac{1}{5}\right)$, with decimal angle $0.19739555985$. That is the same direction as $11.30993247402^{\circ }$.
• There is no i chip in the function bar: the Complex app is off. You can still type $i$ on the ordinary calculation screen, but only the app's chip switches answers to polar form. Open the mode menu and tap the Complex tile.
• An imaginary coefficient appears after i: the calculator can print $2+i\times 3$ for $2+3i$. These mean the same thing; the coefficient is still $3$.