Question

O produto (2+3i) (1-4i) vale:​

(A) 1+11i
(B) 1+31i
(C) 14+5i
(D) 14-5i

Answer 1

$(a + bi) \times (c </strong><strong>+</strong><strong> di) = </strong><strong>\</strong><strong>\</strong><strong> </strong><strong>\</strong><strong>\</strong><strong> </strong><strong>ac</strong><strong> </strong><strong>+</strong><strong> adi + cbi </strong><strong>+</strong><strong>bd</strong><strong> {i }^{2} =</strong><strong> </strong><strong>\</strong><strong>\</strong><strong> </strong><strong>\</strong><strong>\</strong><strong> ac </strong><strong>+</strong><strong> adi + cbi </strong><strong>-</strong><strong> bd = </strong><strong>\</strong><strong>\</strong><strong> </strong><strong>\</strong><strong>\</strong><strong> </strong><strong>(ac </strong><strong>-</strong><strong> bd) </strong><strong>+</strong><strong> (</strong><strong>ad</strong><strong>+</strong><strong>cb</strong><strong>)i \\ \\ </strong><strong>\</strong><strong>\</strong><strong> </strong><strong>Logo</strong><strong>,</strong><strong> </strong><strong>\</strong><strong>\</strong><strong> </strong><strong>(</strong><strong>2</strong><strong>+</strong><strong>3</strong><strong>i</strong><strong>)</strong><strong> </strong><strong>\</strong><strong>t</strong><strong>imes</strong><strong> </strong><strong>(</strong><strong>1</strong><strong>-</strong><strong>4</strong><strong>i</strong><strong>)</strong><strong>=</strong><strong>\</strong><strong>\</strong><strong> </strong><strong> </strong><strong>(</strong><strong>2</strong><strong> </strong><strong>\</strong><strong>t</strong><strong>i</strong><strong>m</strong><strong>e</strong><strong>s</strong><strong> </strong><strong>1</strong><strong> </strong><strong>-</strong><strong> </strong><strong>3</strong><strong> </strong><strong>\</strong><strong>t</strong><strong>i</strong><strong>m</strong><strong>e</strong><strong>s</strong><strong> </strong><strong>(</strong><strong>-</strong><strong>4</strong><strong>)</strong><strong>)</strong><strong>+</strong><strong>(</strong><strong>2</strong><strong> </strong><strong>\</strong><strong>t</strong><strong>i</strong><strong>m</strong><strong>e</strong><strong>s</strong><strong> </strong><strong>(</strong><strong>-</strong><strong>4</strong><strong>)</strong><strong>+</strong><strong>1</strong><strong> </strong><strong>\</strong><strong>t</strong><strong>i</strong><strong>m</strong><strong>e</strong><strong>s</strong><strong> </strong><strong>3</strong><strong>)</strong><strong>i</strong><strong>=</strong><strong> </strong><strong>\</strong><strong>\</strong><strong> </strong><strong>(</strong><strong>2</strong><strong>+</strong><strong>1</strong><strong>2</strong><strong>)</strong><strong>+</strong><strong>(</strong><strong>-</strong><strong>8</strong><strong>+</strong><strong>3</strong><strong>)</strong><strong>i</strong><strong>=</strong><strong>\</strong><strong>\</strong></p><p><strong>1</strong><strong>4</strong><strong>-</strong><strong>5</strong><strong>i</strong><strong>$