Lahenda (3/5-4/5i)(3/5+4/5i)=

$$( \frac { 3 } { 5 } - \frac { 4 } { 5 } i ) ( \frac { 3 } { 5 } + \frac { 4 } { 5 } i ) =$$

Arvuta

$$1$$

Lahenduse etapid

Kompleksarvude \frac{3}{5}-\frac{4}{5}i ja \frac{3}{5}+\frac{4}{5}i korrutamine käib sarnaselt binoomide korrutamisega.

$$\frac{3}{5}\times \frac{3}{5}+\frac{3}{5}\times \left(\frac{4}{5}i\right)-\frac{4}{5}i\times \frac{3}{5}-\frac{4}{5}\times \frac{4}{5}i^{2}$$

i^{2} on -1.

$$\frac{3}{5}\times \frac{3}{5}+\frac{3}{5}\times \left(\frac{4}{5}i\right)-\frac{4}{5}i\times \frac{3}{5}-\frac{4}{5}\times \frac{4}{5}\left(-1\right)$$

Tehke korrutustehted.

$$\frac{9}{25}+\frac{12}{25}i-\frac{12}{25}i+\frac{16}{25}$$

Kombineerige reaal- ja imaginaarosad.

$$\frac{9}{25}+\frac{16}{25}+\left(\frac{12}{25}-\frac{12}{25}\right)i$$

Tehke liitmistehted.

$$1$$

Reaalosa

$$1$$

Lahenduse etapid

Kompleksarvude \frac{3}{5}-\frac{4}{5}i ja \frac{3}{5}+\frac{4}{5}i korrutamine käib sarnaselt binoomide korrutamisega.

$$Re(\frac{3}{5}\times \frac{3}{5}+\frac{3}{5}\times \left(\frac{4}{5}i\right)-\frac{4}{5}i\times \frac{3}{5}-\frac{4}{5}\times \frac{4}{5}i^{2})$$

i^{2} on -1.

$$Re(\frac{3}{5}\times \frac{3}{5}+\frac{3}{5}\times \left(\frac{4}{5}i\right)-\frac{4}{5}i\times \frac{3}{5}-\frac{4}{5}\times \frac{4}{5}\left(-1\right))$$

Tehke korrutustehted võrrandis \frac{3}{5}\times \frac{3}{5}+\frac{3}{5}\times \left(\frac{4}{5}i\right)-\frac{4}{5}i\times \frac{3}{5}-\frac{4}{5}\times \frac{4}{5}\left(-1\right).

$$Re(\frac{9}{25}+\frac{12}{25}i-\frac{12}{25}i+\frac{16}{25})$$

Kombineerige võrrandis \frac{9}{25}+\frac{12}{25}i-\frac{12}{25}i+\frac{16}{25} reaal- ja imaginaarosad.

$$Re(\frac{9}{25}+\frac{16}{25}+\left(\frac{12}{25}-\frac{12}{25}\right)i)$$

Tehke liitmistehted võrrandis \frac{9}{25}+\frac{16}{25}+\left(\frac{12}{25}-\frac{12}{25}\right)i.

$$Re(1)$$

Arvu 1 reaalosa on 1.

$$1$$