Question

In the above figure Z represent a complex number. a. Write the complex number in polar form. b. Find real and imaginary parts of Z. c. Find multiplicative inverse of Z in the form a+ib.

Answer 1

The complex number in polar form is 5∠53.13°. The real and imaginary parts of Z = 3,4. The multiplicative inverse of Z is $\frac{3}{25} - i\frac{4}{25}$.

• Given,
• Z=3+i4 (assumption)
• $r=\sqrt {3^2+4^2} = 5$
• ∅ $=tan^{-1} \frac{4}{3}$
• =53.13°
• The complex number in polar form is 5∠53.13°
• Now,
• Z=3+i4
• real number = 3
• imaginary number = 4
• Now,

• The multiplicative inverse of Z
• $=\dfrac{1}{3+4i}\\\\=\dfrac{1}{3+4i} * \dfrac{3-4i}{3-4i}\\\\=\dfrac{3}{25} - i \dfrac{4}{25}$