Issolvi 4i/1-2i+1-i/1+2i+12/5

$$\frac { 4 i } { 1 - 2 i } + \frac { 1 - i } { 1 + 2 i } + \frac { 12 } { 5 }$$

Evalwa

$$\frac{3}{5}+\frac{1}{5}i=0.6+0.2i$$

Passi tas-Soluzzjonijiet

Immultiplika kemm in-numeratur u d-denominatur ta' \frac{4i}{1-2i} bil-konjugat kumpless tad-denominatur, 1+2i.

$$\frac{4i\left(1+2i\right)}{\left(1-2i\right)\left(1+2i\right)}+\frac{1-i}{1+2i}+\frac{12}{5}$$

Agħmel il-multiplikazzjonijiet fi \frac{4i\left(1+2i\right)}{\left(1-2i\right)\left(1+2i\right)}.

$$\frac{-8+4i}{5}+\frac{1-i}{1+2i}+\frac{12}{5}$$

Iddividi -8+4i b'5 biex tikseb-\frac{8}{5}+\frac{4}{5}i.

$$-\frac{8}{5}+\frac{4}{5}i+\frac{1-i}{1+2i}+\frac{12}{5}$$

Agħmel l-addizzjonijiet.

$$\frac{1-i}{1+2i}+\frac{4}{5}+\frac{4}{5}i$$

Immultiplika kemm in-numeratur u d-denominatur ta' \frac{1-i}{1+2i} bil-konjugat kumpless tad-denominatur, 1-2i.

$$\frac{\left(1-i\right)\left(1-2i\right)}{\left(1+2i\right)\left(1-2i\right)}+\frac{4}{5}+\frac{4}{5}i$$

Agħmel il-multiplikazzjonijiet fi \frac{\left(1-i\right)\left(1-2i\right)}{\left(1+2i\right)\left(1-2i\right)}.

$$\frac{-1-3i}{5}+\frac{4}{5}+\frac{4}{5}i$$

Iddividi -1-3i b'5 biex tikseb-\frac{1}{5}-\frac{3}{5}i.

$$-\frac{1}{5}-\frac{3}{5}i+\frac{4}{5}+\frac{4}{5}i$$

Agħmel l-addizzjonijiet.

$$\frac{3}{5}+\frac{1}{5}i$$

Parti Reali

$$\frac{3}{5} = 0.6$$

Passi tas-Soluzzjonijiet

Immultiplika kemm in-numeratur u d-denominatur ta' \frac{4i}{1-2i} bil-konjugat kumpless tad-denominatur, 1+2i.

$$Re(\frac{4i\left(1+2i\right)}{\left(1-2i\right)\left(1+2i\right)}+\frac{1-i}{1+2i}+\frac{12}{5})$$

Agħmel il-multiplikazzjonijiet fi \frac{4i\left(1+2i\right)}{\left(1-2i\right)\left(1+2i\right)}.

$$Re(\frac{-8+4i}{5}+\frac{1-i}{1+2i}+\frac{12}{5})$$

Iddividi -8+4i b'5 biex tikseb-\frac{8}{5}+\frac{4}{5}i.

$$Re(-\frac{8}{5}+\frac{4}{5}i+\frac{1-i}{1+2i}+\frac{12}{5})$$

Agħmel l-addizzjonijiet fi -\frac{8}{5}+\frac{4}{5}i+\frac{12}{5}.

$$Re(\frac{1-i}{1+2i}+\frac{4}{5}+\frac{4}{5}i)$$

Immultiplika kemm in-numeratur u d-denominatur ta' \frac{1-i}{1+2i} bil-konjugat kumpless tad-denominatur, 1-2i.

$$Re(\frac{\left(1-i\right)\left(1-2i\right)}{\left(1+2i\right)\left(1-2i\right)}+\frac{4}{5}+\frac{4}{5}i)$$

Agħmel il-multiplikazzjonijiet fi \frac{\left(1-i\right)\left(1-2i\right)}{\left(1+2i\right)\left(1-2i\right)}.

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

Iddividi -1-3i b'5 biex tikseb-\frac{1}{5}-\frac{3}{5}i.

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

Agħmel l-addizzjonijiet fi -\frac{1}{5}-\frac{3}{5}i+\frac{4}{5}+\frac{4}{5}i.

$$Re(\frac{3}{5}+\frac{1}{5}i)$$

Il-parti reali ta' \frac{3}{5}+\frac{1}{5}i hija \frac{3}{5}.

$$\frac{3}{5}$$