Express the complex number (1+i)/(2-i) in Cartesian form.

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To express the complex number (z₁)/(z₂) in Cartesian form, we multiply the numerator and the denominator by the conjugate of the denominator. Step 1: Identify the complex numbers z₁ and z₂. We are given z₁ = 1+i and z₂ = 2−i. Step 2: Set up the division. (z₁)/(z₂) = (1+i)/(2−i) Step 3: Multiply the numerator and denominator by the conjugate of the denominator. The denominator is 2−i. Its conjugate is 2+i. (1+i)/(2−i) × (2+i)/(2+i) Step 4: Expand the numerator. (1+i)(2+i) = 1(2) + 1(i) + i(2) + i(i); = 2 + i + 2i + i²; Since i² = −1: = 2 + 3i − 1; = 1 + 3i Step 5: Expand the denominator. (2−i)(2+i) = 2² − (i)²; = 4 − i²; Since i² = −1: = 4 − (−1); = 4 + 1 = 5 Step 6: Combine the simplified numerator and denominator. (1+3i)/(5) Step 7: Express in Cartesian form a+bi. 1/5 + 3/5i The Cartesian form is 1/5 + 3/5i.

Express the complex number (1+i)/(2-i) in Cartesian form.

Answer

Step-by-step solution

Identify the complex numbers $z_1$ and $z_2$ .

Set up the division.

Multiply the numerator and denominator by the conjugate of the denominator.

Expand the numerator.

Expand the denominator.

Combine the simplified numerator and denominator.

Express in Cartesian form $a+bi$ .

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Express the complex number (1+i)/(2-i) in Cartesian form.

Answer

Step-by-step solution

Identify the complex numbers z1z_1z1​ and z2z_2z2​.

Set up the division.

Multiply the numerator and denominator by the conjugate of the denominator.

Expand the numerator.

Expand the denominator.

Combine the simplified numerator and denominator.

Express in Cartesian form a+bia+bia+bi.

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More Mathematics Questions

Identify the complex numbers $z_1$ and $z_2$ .

Express in Cartesian form $a+bi$ .