Basic Operations

For addition, subtraction, multiplication, and division write the expressions in standard form and apply Evaluate. Scientific Notebook will return the result in the form a + bi or a + ib, with a and b real numbers.

$\blacktriangleright$ Evaluate

$\sqrt{{-5}}$ =  i$\sqrt{{5}}$

$\left(\vphantom{ 1+i}\right.$1 + i$\left.\vphantom{ 1+i}\right)$$\left(\vphantom{ 3-2i}\right.$3 - 2i$\left.\vphantom{ 3-2i}\right)$ =  5 + i 6pt

${\dfrac{{i}}{{1+i}}}$ =  ${\dfrac{{1}}{{2}}}$ + ${\dfrac{{1}}{{2}}}$i 6pt

$\left(\vphantom{ 23-5i}\right.$23 - 5i$\left.\vphantom{ 23-5i}\right)$ + $\left(\vphantom{ 1+16i}\right.$1 + 16i$\left.\vphantom{ 1+16i}\right)$ = 24 + 11i


$\left(\vphantom{ 2.5+3i}\right.$2.5 + 3i$\left.\vphantom{ 2.5+3i}\right)$ - $\left(\vphantom{ 3.59+16i}\right.$3.59 + 16i$\left.\vphantom{ 3.59+16i}\right)$ = -1. 09 - 13.0i


$\left(\vphantom{ 2.5+3i}\right.$2.5 + 3i$\left.\vphantom{ 2.5+3i}\right)$$\left(\vphantom{ 3.59+16i}\right.$3.59 + 16i$\left.\vphantom{ 3.59+16i}\right)$ = -39. 025 + 50. 77i


$\left(\vphantom{ 23-5i}\right.$23 - 5i$\left.\vphantom{ 23-5i}\right)$/$\left(\vphantom{ 1+16i}\right.$1 + 16i$\left.\vphantom{ 1+16i}\right)$ = - ${\frac{{57}}{{257}}}$ - ${\frac{{% 373}}{{257}}}$i


${\frac{{2.5+3i}}{{3.59+16i}}}$ = . 21189 - . 10871i


$\left(\vphantom{ 1+16i}\right.$1 + 16i$\left.\vphantom{ 1+16i}\right)$$\left(\vphantom{ \left( 2.5+3i\right) -\left( 3.59+16i\right) }\right.$$\left(\vphantom{ 2.5+3i}\right.$2.5 + 3i$\left.\vphantom{ 2.5+3i}\right)$ - $\left(\vphantom{ 3.59+16i}\right.$3.59 + 16i$\left.\vphantom{ 3.59+16i}\right)$$\left.\vphantom{ \left( 2.5+3i\right) -\left( 3.59+16i\right) }\right)$ = 206. 91 - 30. 44i

Note    For some of the expressions with complex numbers, the keyboard shortcut CTRL + E for evaluation is not as effective as the menu item Evaluate.